TWI533236B

TWI533236B - A method of cs-waveletbased image coding for dvc system

Info

Publication number: TWI533236B
Application number: TW101140560A
Authority: TW
Inventors: 沈岱範; 程彥明
Original assignee: 國立雲林科技大學
Priority date: 2012-11-01
Filing date: 2012-11-01
Publication date: 2016-05-11
Also published as: TW201419860A

Description

小波壓縮感測影像編碼之方法 Wavelet compression sensing image coding method

本發明係涉及影像壓縮處理的方法，尤指係針對小波壓縮感測的編碼方式進行改良，以提升影像重建速度及其品質的一種影像壓縮編碼的方法，同時本發明亦可適用於分散式影像視訊編碼系統。 The invention relates to a method for image compression processing, in particular to a method for image compression coding which improves the coding mode of wavelet compression sensing to improve image reconstruction speed and quality, and the invention can also be applied to distributed image. Video coding system.

首先最傳統的影像編碼架構如第73圖所示，一開始進行取樣再來壓縮，然後經過儲存與傳輸，最後到解碼端接收後再解壓縮。再來看到壓縮感測(compressing sensing，簡稱CS)基本架構如第74圖所示，在該壓縮感測步驟時已經完成取樣及壓縮的動作，然後一樣儲存與傳輸，最後到解碼端接收後再重建。接續，將傳統編碼架構及CS基本架構作結合如第75圖所示的CS改良式架構，一開始一樣有取樣，但是在壓縮時，變更為CS的隨機取樣，然後儲存及傳輸，接收後再進行CS重建的工作，目的是利用CS編碼端是非常簡單，來取代傳統的編碼，以利發展分散式視訊編碼器(Distributed Vedio Coding，簡稱DVC)，因為DVC系統是很多個編碼器對上單一解碼器，跟傳統的影像或視訊編碼(如JPEG、JPEG2000)是不一樣的，DVC只要簡單的解碼器，這樣可以降低成本，解碼器是可以複雜的。 First, the most traditional image coding architecture, as shown in Figure 73, is initially sampled and then compressed, then stored and transmitted, and finally decompressed after being received by the decoder. Then, the basic structure of the compression sensing (CS) is shown in FIG. 74. The sampling and compression operations have been completed during the compression sensing step, and then stored and transmitted in the same manner, and finally received by the decoder. Rebuild. In the continuation, the traditional coding architecture and the CS basic architecture are combined. The CS modified architecture shown in Figure 75 has the same sampling at the beginning, but when compressed, it is changed to CS random sampling, then stored and transmitted, and then received. The purpose of CS reconstruction is to use the CS encoding end to replace the traditional encoding to facilitate the development of Distributed Video Coding (DVC), because the DVC system is a single encoder pair. The decoder is different from traditional video or video encoding (such as JPEG, JPEG2000). DVC only needs a simple decoder, which can be reduced to This, the decoder can be complicated.

另由由本發明人申請本國發明專利，且經編列第100102685號的『基於小波轉換域訊號與人眼視覺特性之壓縮取樣影像編碼技術及其性能評估方法』。該案係使用離散小波(Discrete Wavelet Transformation，簡稱DWT)的Daubechies(9,7)filter，再重建部分則使用梯度投影稀疏重構(Gradient Projection Sparse Reconstruction，簡稱GPSR)的重建方法。 In addition, the present inventors apply for a national invention patent, and the "compressed sampling image coding technology based on wavelet transform domain signal and human visual characteristics and its performance evaluation method" is listed in No. 100102685. The case uses the Daubechies (9,7) filter of Discrete Wavelet Transformation (DWT), and the reconstruction part uses the Gradient Projection Sparse Reconstruction (GPSR) reconstruction method.

又該案更使用了下述影像編碼技巧：(1)、採用BF當作CS的量測方法；(2)、採用五階段小波轉換；(3)、使用DWT當作CS的稀疏基；(4)、運用小波域的性號特性；(5)、運用了小波轉換後的HL/LH頻帶係數的方向性；(6)使用了JDN量化於小波的次頻帶；(7)分配權重至次頻帶。 The case also uses the following image coding techniques: (1), using BF as the measurement method of CS; (2) using five-stage wavelet transform; (3) using DWT as the sparse basis of CS; 4), using the characteristics of the wavelet domain; (5), using the directionality of the HL/LH band coefficients after wavelet transform; (6) using JDN to quantize the sub-band of the wavelet; (7) assigning weights to the next frequency band.

如第76圖所示者，特別一提，該案的特色係其壓縮取樣的量測向量未經過量測矩陣隨機取得，而係以各次頻帶之間的訊號特徵(稀疏性和均勻性)來分配量測向量的大小，初步分配給五階小波轉換後各次頻帶的權重LL(包含LL5、HL5、LH5，...，LH2、HH2)、HL、LH、HH分別獲得M/2、M/5、M/5、M/10。 As shown in Fig. 76, in particular, the feature of the case is that the measurement vector of the compressed sample is randomly obtained without the over-measurement matrix, and the signal characteristics (sparseness and uniformity) between the sub-bands are used. To allocate the magnitude of the measurement vector, initially assigned to the weight LL (including LL5, HL5, LH5, ..., LH2, HH2), HL, LH, HH of each frequency band after the fifth-order wavelet transform, and obtain M/2 respectively. M/5, M/5, M/10.

因此，該案係以編碼觀點、信號的特性，據以提出小波的方向性、各個頻帶的重要性以及量化觀念，以lena512^＊512來說，可以在相同Bit_Rate下，JND-Q+W+D的架構下，該PSNR值會比原始CS隨機取樣架構高出3.5db到6db左右(0.75bpp到1.75bpp)，而在計算量上只比原始CS隨機取樣架構多花了6%到18%而已。 Therefore, the case is based on the characteristics of the coding viewpoint and signal, and the directionality of the wavelet, the importance of each frequency band, and the quantitative concept are proposed. In the case of lena512 ^* 512, it can be under the same Bit_Rate, JND-Q+W+D. The PSNR value is 3.5db to 6db (0.75bpp to 1.75bpp) higher than the original CS random sampling architecture, and only 6% to 18% more computationally than the original CS random sampling architecture. .

鑒於為解決上述問題及滿足影像的快速編碼儲存、快速影像傳輸、其壓縮重建後影像的品質之目的，本發明人乃憑恃著長期對影像編碼技術之構思，而發明出一種小波壓縮感測影像的編碼方法，其方法步驟係包含有：(a).輸入一張圖片，其解析度為m×n；(b).進行多階小波轉換；(c)各頻帶分別進行純量量化；(d)計算各頻帶的非零係數比並分配各次頻帶權重；(e).針對各頻帶去進行壓縮感測處理後，再經round處理；(f)分別送到霍夫曼編碼。 In order to solve the above problems and satisfy the purpose of fast code storage and fast image transmission, and image quality after compression and reconstruction, the present inventors have invented a wavelet compression sensing image with the long-term conception of image coding technology. The coding method includes the following steps: (a) inputting a picture with a resolution of m×n; (b) performing multi-order wavelet conversion; and (c) performing scalar quantization on each frequency band; d) calculating the non-zero coefficient ratio of each frequency band and assigning each sub-band weight; (e) performing compression sensing processing for each frequency band, and then performing round processing; (f) respectively sending to Huffman coding.

而本發明方法係另包含一解碼方法，其中該解碼方法係包含有以下步驟：(g).將接收到的霍夫曼編碼以進行霍夫曼解碼；(h).分別對各個頻帶進行梯度投影稀疏重建；(i).分別對各個頻帶進行反量化；(j).把各個頻帶合成一個矩陣進行反小波轉換；(k).重建影像並計算其峰值訊噪比值完成後，輸出該影像。 The method of the present invention further includes a decoding method, wherein the decoding method includes the following steps: (g) receiving the Huffman code for Huffman decoding; (h) separately performing gradients on each frequency band. Projection sparse reconstruction; (i) inversely quantizing each frequency band separately; (j) combining each frequency band into a matrix for inverse wavelet transform; (k) after reconstructing the image and calculating the peak signal to noise ratio value, outputting the image .

而上述所述round處理係為：NZR_band×M=round(NZR_band×m×n×MR)；上述公式中，該NZR_band係指各頻帶的非零係數比，該M=m×n×MR為總取樣個數，該MR係為給定的量測值，最後經過round四捨五入變成整數。 The round processing described above is: NZR_band×M=round (NZR_band×m×n×MR); in the above formula, the NZR_band refers to a non-zero coefficient ratio of each frequency band, and the M=m×n×MR is total The number of samples, the MR is a given measurement, and finally rounded to round to round to an integer.

茲由以上說明得知，本發明方法相較先前技術，確可達到如下之功效增進： From the above description, it is known that the method of the present invention achieves the following enhancements compared to the prior art:

1.本發明方法在相同的Bit_Rate下，加入非零係數比(non-zero-ratio)分配的架構，雖然計算量上有大幅提升，但是品質會比原始隨機分配架構高出10db左右。 1. The method of the present invention adds a non-zero-ratio allocation architecture under the same Bit_Rate, although the amount of computation is greatly improved, but the quality It will be about 10db higher than the original random allocation architecture.

2.本發明方法，若頻帶分配到的MR較高時，次頻帶所有係數做直接傳送的效果可能比經過CS還要好，在相同Bit_Rate下，影像品質會高出12db左右。 2. In the method of the present invention, if the MR assigned to the frequency band is high, the effect of direct transmission of all coefficients of the sub-band may be better than that of the CS, and the image quality will be about 12 db higher under the same Bit_Rate.

3.本發明方法若以趨近於零值的HH1直接用零矩陣取代時，品質最多不會相差超過0.5db。 3. If the method of the present invention is directly replaced by a zero matrix with HH1 approaching zero, the quality will not differ by more than 0.5 db at most.

4.另外本發明方法也跟文獻[7]做比較，在相同的條件下，文獻[7]的lena結果是28.39db，而本發明的是32.10db，文獻[7]的boat的結果是25.84db，本發明的是33.86db，明顯可以看到增加許多。 4. In addition, the method of the present invention is also compared with the literature [7]. Under the same conditions, the lena result of the literature [7] is 28.39db, while the invention is 32.10db, and the result of the boat of the literature [7] is 25.84. Db, the invention is 33.86db, obviously can be seen to increase a lot.

5.本發明與現今JPEG及JPEG2000的編碼方法作比較，雖本發明方法的影像品質都較低，但是在其編碼複雜度方面，本發明方法所發展的架構要比JPEG2000還要快1779%，故本發明方法將有利於發展分散式視訊技術(DVC)。 5. The present invention compares with the current JPEG and JPEG2000 encoding methods. Although the image quality of the method of the present invention is low, the architecture developed by the method of the present invention is 1779% faster than JPEG2000 in terms of its encoding complexity. Therefore, the method of the present invention will facilitate the development of distributed video technology (DVC).

為進一步說明本發明上述目的、所運用方法及其所達成功效，本發明人將予以詳細說明如后：請參閱第1圖所示，本發明系關於一種小波壓縮感測影像的編碼方法，其方法步驟係包含有：(a).輸入一張圖片，其解析度為m×n；(b).進行多階小波轉換；(c)各頻帶分別進行純量量化；(d)計算各頻帶的非零係數比並分配各次頻帶權重；(e).針對各頻帶去進行壓縮感測處理後，再經round處理；(f)分別送到霍夫曼編碼。 To further illustrate the above objects, methods of use, and effects achieved by the present invention, the inventors will be described in detail as follows: Referring to FIG. 1, the present invention relates to a method for encoding wavelet compression sensing images. The method steps include: (a) inputting a picture with a resolution of m×n; (b) performing multi-order wavelet conversion; (c) performing scalar quantization on each frequency band; (d) calculating each frequency band The non-zero coefficient ratio is assigned to each sub-band weight; (e). After performing compression sensing processing for each frequency band, it is processed by round; (f) is sent to Huffman coding separately.

請參閱第2圖所示，另本發明對應前述編碼的方法，亦設有一解碼方法，其中該解碼方法係包含有以下步驟：(g).將接收到的霍夫曼編碼以進行霍夫曼解碼；(h).分別對各個頻帶進行梯度投影稀疏重建；(i).分別對各個頻帶進行反量化；(j).把各個頻帶合成一個矩陣進行反小波轉換；(k).重建影像並計算其峰值訊噪比值完成後，輸出該影像。 Referring to FIG. 2, the present invention further corresponds to the foregoing encoding method, and a decoding method is also provided. The decoding method includes the following steps: (g). The received Huffman encoding is performed by Huffman. Decoding; (h) separately performing gradient projection sparse reconstruction on each frequency band; (i) separately performing inverse quantization on each frequency band; (j) combining each frequency band into a matrix for inverse wavelet transform; (k) reconstructing the image and After the peak signal to noise ratio value is calculated, the image is output.

茲分別對上述本發明方法的編碼步驟分別詳述如下： The coding steps of the above method of the invention are respectively detailed as follows:

步驟(a).輸入一張圖片，其解析度為m×n： Step (a). Enter a picture with a resolution of m×n:

電腦上的圖片影像是利用影像的小方格就是所謂的像素(Pixel)所構成的，這些小方格是影像中最小的單位，每一個小方格都有一個明確的位置，和單一的色彩，而這些一格格的位置和色彩就決定了該圖片影像所呈現出來的樣子。 The image on the computer is made up of small squares of pixels called Pixels. These small squares are the smallest units in the image. Each small square has a clear position and a single color. And the position and color of these one grids determine what the image of the picture looks like.

而所謂解析度，指的是單位長度上像素的數目，單位可分「像素/英吋」或是「像素/公分」(pixels/inch；pixels/cm)。解析度的設定是決定列印輸出品質的重要因素，高解析度的影像運用較多的像素，所以可呈現出比低解析度影像更細膩的色調變化，相對的檔案體積也更大。因此一張圖片影像的像素總數可以m×n表示，例如上圖的像素總量為：400(寬)X 561(高)=224400。 The so-called resolution refers to the number of pixels per unit length. The unit can be divided into "pixels/miles" or "pixels/cm" (pixels/inch; pixels/cm). The resolution setting is an important factor in determining the print output quality. High-resolution images use more pixels, so they can exhibit more subtle color changes than low-resolution images, and the relative file size is larger. Therefore, the total number of pixels of a picture image can be expressed by m×n. For example, the total number of pixels in the above figure is: 400 (width) X 561 (high)=224400.

步驟(b).進行多階小波轉換： Step (b). Perform multi-order wavelet conversion:

現有的小波壓縮感測技術在影像編碼上具有非常低的複雜度，但是如果實際來運用的話，他的R-D效能卻是非常低的。因此本發明係利用變換域的信號特性和量化方法，讓信號不僅變稀疏，而且具有較低的編碼訊息量，最後目的是利用壓縮感測編碼端的簡單編碼來降低成本，進而發展分散式視訊編碼器DVC(Distributed Video Coding)。 The existing wavelet compression sensing technology has very low complexity in image coding, but if it is actually used, his R-D performance is very low. Therefore, the present invention utilizes the signal characteristics and quantization methods of the transform domain to make the signal not only sparse, Moreover, it has a lower amount of encoded information, and the final purpose is to reduce the cost by using simple coding of the compression sensing encoder, thereby developing a distributed video encoder DVC (Distributed Video Coding).

一、壓縮感測架構： First, the compression sensing architecture:

通常小波壓縮感測(CS理論)架構主要包括訊號的稀疏表示、編碼量測模型、解碼重建模型等這三個方面。分別說明如下： Generally, the wavelet compression sensing (CS theory) architecture mainly includes three aspects: sparse representation of signals, coding measurement model, and decoding reconstruction model. Explain as follows:

1.信號的稀疏表示： 1. Sparse representation of the signal:

請參閱第3圖所示，CS理論的前提條件是訊號具有稀疏性(Sparsity)或可壓縮性(Compressible)，考慮長度為N的離散實值信號，記為x，n[1,2,...,N]。由訊號理論可知x能够用一組基Ψ^T=[Ψ₁,Ψ₂,...,Ψ_m,...,Ψ_M]的線性組合表示(其中Ψ^T代表Ψ的轉置)，式2.1中：α_k=〈x,Ψ_K〉，α與是N×1矩陣，Ψ是k矩陣。當訊號x在某個基Ψ上僅有α=Ψ x個非零係數(或遠大於零的係數)α_K時，稱Ψ為訊號x的稀疏基。信號在稀疏基上只有k個非零係數屬於嚴格稀疏的情況，多數情況下訊號無法滿足嚴格稀疏的要求，但仍具有可壓縮性，即訊號的轉換係數經排序後可以指數進行衰減趨近於零時，訊號也是可以近似稀疏表示的。合理選擇稀疏基Ψ，使得訊號的稀疏係數盡可能減少，不僅有利於提高採集訊號的速度，且有利於減少傳輸信號所佔用的資源。常用的稀疏基有：正(餘) 弦基、小波基、chirplet基以及curvelet基等。 Referring to Figure 3, the premise of the CS theory is that the signal has Sparsity or Compressible. Consider a discrete real-valued signal of length N, denoted as x, n. [1,2,...,N]. It can be seen from the signal theory that x can be represented by a linear combination of a set of bases ^T = [Ψ ₁ , Ψ ₂ , ..., Ψ _m , ..., Ψ _M ] (where Ψ ^T represents the transposition of Ψ), In Equation 2.1: α _k = < x, Ψ _K 〉, α is an N × 1 matrix, and Ψ is a k matrix. When the signal x has only α=Ψ x non-zero coefficients (or a coefficient much larger than zero) α _K on a certain basis, it is called a sparse basis of the signal x. The signal has only k non-zero coefficients on the sparse basis. It is strictly sparse. In most cases, the signal cannot meet the strict sparsity requirement, but it is still compressible. That is, the signal conversion coefficient can be exponentially attenuated to be close to At zero hour, the signal can also be approximated sparsely. Reasonable selection of the sparse basis makes the signal's sparse coefficient as small as possible, which not only helps to increase the speed of collecting signals, but also helps to reduce the resources occupied by the transmitted signals. Commonly used sparse bases are: positive (remaining) string base, wavelet base, chirplet base, and curvelet base.

2. CS量測編碼模型： 2. CS measurement coding model:

請參閱第4圖所示，在CS編碼量測模型中並不是直接量測稀疏信號x本身，而是將信號x投影到一組量測向量 s.t.y=ΦΨα上，而得到量測值，y_m=〈x,φ^T _m〉。寫成矩陣形式為y=Φx (式2.2)式2.2中：x是N×1矩陣，y是M×1矩陣，Φ是M×N的量測矩陣。將式2.1代入式2.2會得到y=Φx=ΦΨα=Θα (式2.3) Referring to FIG. 4, in the CS coding measurement model, the sparse signal x itself is not directly measured, but the signal x is projected onto a set of measurement vectors. On sty=ΦΨα, the measured value is obtained, y _m =<x, φ ^T _m 〉. Write the matrix form as y = Φx (Equation 2.2) In Equation 2.2: x is an N × 1 matrix, y is an M × 1 matrix, and Φ is a measurement matrix of M × N. Substituting Equation 2.1 into Equation 2.2 yields y = Φx = Φ Ψ α = Θ α (Equation 2.3)

請參閱第5圖所示，式2.3中：Θ=ΦΨ是M×N矩陣。由於量測值維數M遠遠小於信號維數N，求解式2.2的逆問題是一個病態問題，所以無法直接從y的M個量測值中解出信號x。而由於式2.3中α是k稀疏的，即僅有k個非零數，而且k<M<<N，那麼利用訊號稀疏分解理論中已有的稀疏分解演算法，可以通過求解式2.3的逆問題得到稀疏係數α，再帶回式2.1進一步得到訊號x。Candes等人指出為了保證算法上的收斂性，使得k個係數能夠由M個量測值準確的恢復，式2.3中矩陣Θ必須滿足受限等距特性(restricted isometry property,RIP)準則，即對於任意具有嚴格k稀疏(可壓縮情況下要求為3k)的向量v，矩陣Θ都能保證如式2.4之不等式成立式2.4中ε必須要大於零。RIP準則的一種等價的情況是量測矩陣Φ和稀疏矩陣Ψ滿足不相關特性的要求(Incoherence)。實際量測中稀疏基Ψ可能會因訊號的不同而改變，因此本發明希望找到對任意的稀疏基Ψ都能滿足和量測基Φ不相關。對一維訊號而言，量測矩陣Φ選取服從高斯分佈的基向量能保證和任意稀疏基Ψ不相關的機率很高。故實際中一般採用隨機矩陣進行量測，常見的有二值量測矩陣、複利葉量測矩陣即不相關測量矩陣等。當然，隨著壓縮感測理論的發展，還可能湧出更多的隨機量測方式或方法。 Please refer to Figure 5, in Equation 2.3: Θ = Φ Ψ is an M × N matrix. Since the dimension M of the measured value is much smaller than the signal dimension N, solving the inverse problem of Equation 2.2 is a ill-conditioned problem, so the signal x cannot be directly solved from the M measured values of y. Since α is k sparse in Equation 2.3, that is, there are only k non-zero numbers, and k<M<<N, then the existing sparse decomposition algorithm in the signal sparse decomposition theory can be solved by solving the inverse of Equation 2.3. The problem is obtained by the sparse coefficient α, and then brought back to Equation 2.1 to further obtain the signal x. Candes et al. pointed out that in order to ensure the convergence of the algorithm, k coefficients can be accurately recovered by M measurements. The matrix 式 in Equation 2.3 must satisfy the restricted isometry property (RIP) criterion, ie Any vector v with strict k sparsity (requires 3k in compressible case), matrix Θ can guarantee the inequality of equation 2.4 In Equation 2.4, ε must be greater than zero. An equivalent case of the RIP criterion is that the measurement matrix Φ and the sparse matrix Ψ satisfy the requirement of irrelevant characteristics (Incoherence). In the actual measurement, the sparse basis may change due to the difference of the signal, so the present invention hopes to find that any of the sparse bases can be satisfied and the measurement base Φ is irrelevant. For the one-dimensional signal, the measurement matrix Φ selects the base vector obeying the Gaussian distribution to ensure that the probability of being unrelated to any sparse basis is high. Therefore, in practice, a random matrix is generally used for measurement. Commonly, there are a binary measurement matrix, a compound leaf measurement matrix, that is, an uncorrelated measurement matrix. Of course, with the development of compression sensing theory, more random measurement methods or methods may emerge.

3. CS解碼重建模型 3. CS decoding reconstruction model

當式2.3中的矩陣Θ滿足RIP準則時，CS理論能夠通過對式2.3的逆問題先求解稀疏係數α=Ψ^T x後代入式2.1將稀疏度為k的訊號x從M維的量測投影值y中正確地恢復出來。解碼的最直接方法是透過l₀範數下求解式2.3的最優化問題從而得到稀疏係數的估計。由於式2.5的求解釋個NP-hard問題，而該最優化問題與訊號的稀疏分解十分類似，所已有學者從訊號稀疏分解的相關理論中尋找更有效的求解途徑。文獻[1]表明l₁最小範數下在一定條件下和l₀最小範數具有等價性，可得到相同的解。那麼式2.5轉化為l₁最小範數下的最優化問題稍微的差別使得問題變成了一個凸優化問題(Convex Optimization)，於是可以方便地化簡為線性規劃的問題。l₁最小範數下最優化問題又稱為基追蹤(Basic Pursuit,BP)文獻[2]，儘管BP算法可行，但在實際應用中存在二個問題：第一，即使是常見的圖片尺寸，計算量複雜度很高，取樣點個數滿足Mlog₂ 時，重建計算複雜度的量級在O(N³)。第二，由於l₁範數無法區分稀疏係數尺度位置，所以儘管整體上重建訊號在歐氏距離上逼近訊號，但存在低尺度能量般移到了高尺度的現象，從而容易出現一些人工效應，如一維訊號會在高頻出現震盪。由於l₁最小範數下的算法速度較慢，新的快速貪婪法被逐漸採用，通過局部最優化依次找到各個非零係數，如正交匹配追蹤(Orthogonal Matching Pursuit,OMP)文獻[3]等，這些算法的計算複雜度比BP方法低，但需要更多的觀測值及更大儲存空間。此外，還有很多其他種類的算法，如內點法(Interior Point)文獻[4]、梯度投影法(Gradient Projection Sparse Reconstruction,GPSR)文獻[5]、分段正交匹配追蹤(Stage-wise OMP,StOMP)文獻[6]等。 When the matrix 式 in Equation 2.3 satisfies the RIP criterion, the CS theory can solve the inverse problem of Equation 2.3 by first solving the sparse coefficient α=Ψ ^T x and then using the 2.1 to measure the signal x with the sparsity of k from the M dimension. The value y is correctly restored. The most straightforward method of decoding is to solve the optimization problem of Equation 2.3 by using the l ₀ norm. Thereby an estimate of the sparse coefficient is obtained. Since Equation 2.5 solves the NP-hard problem, and the optimization problem is very similar to the sparse decomposition of the signal, some scholars have found a more effective solution path from the related theory of signal sparse decomposition. [1] showed that L ₁ equivalent with the minimum norm under certain conditions and minimum norm l _0, the same solution can be obtained. Then Equation 2.5 is transformed into an optimization problem under the minimum norm of l ₁ A slight difference makes the problem a Convex Optimization problem, which can be easily reduced to a linear programming problem. l _{1 The} minimum norm optimization problem is also called the Basic Pursuit (BP) literature [2]. Although the BP algorithm is feasible, there are two problems in practical applications: first, even the common picture size, The calculation amount is very complicated, and the number of sampling points satisfies M Log ₂ When reconstructed, the computational complexity is on the order of O(N ³ ). Second, since the l ₁ norm cannot distinguish the scale position of the sparse coefficient, although the reconstruction signal as a whole approaches the signal at the Euclidean distance, there is a phenomenon that the low-scale energy moves to a high scale, and thus some artificial effects are easily generated, such as The Weixin number will oscillate at high frequencies. Since the speed of the algorithm at a slower minimum norm l _1, new fast greedy method is gradually adopted, found via the respective local optimization order nonzero coefficient, such as orthogonal matching pursuit (Orthogonal Matching Pursuit, OMP) in [3] These algorithms have lower computational complexity than the BP method, but require more observations and more storage space. In addition, there are many other kinds of algorithms, such as Interior Point (4), Gradient Projection Sparse Reconstruction (GPSR) [5], and segmentation orthogonal matching (Stage-wise OMP). , StOMP) literature [6] and so on.

二、評估CS的四種量測方法： Second, evaluate the four measurement methods of CS:

本發明係使用的CS是由John Hopkins University Thong Do所提出的文獻[8]，它們的Transform是使用DWT的Daubechies(9,7)filter文獻[9]，再重建部分是使用GPSR(Gradient Projection Sparse Reconstruction)的重建方法。在CS量測方法有四種，分別為BF,SFFT,Ha512 and DCT512，輸入圖片是lena，大小為512^＊512，將會比較R-D效能及複雜度。 The CS used in the present invention is a document proposed by John Hopkins University Thong Do [8], their Transform is a Daubechies (9,7) filter using DWT [9], and the reconstruction part is using GPSR (Gradient Projection Sparse). Reconstruction) reconstruction method. There are four methods for measuring CS, namely BF, SFFT, Ha512 and DCT512. The input picture is lena and the size is 512 ^* 512, which will compare RD performance and complexity.

由第6圖及第7圖所示，可以看到BF方法的R-D效能，比其他三種都好，而複雜度也是比其他人低的，因此本發明係採用BF當作CS的量測方法。 From Figure 6 and Figure 7, we can see the R-D performance of the BF method. All three are good, and the complexity is lower than others. Therefore, the present invention uses BF as a measurement method of CS.

三、評估CS_wavelet小波轉換階數： Third, evaluate the CS_wavelet wavelet transform order:

在這裡本發明評估要以多少階的小波轉換來用在CS中，因為不同的小波階層，子頻帶的總數也有所不同，例如4階小波轉換有13個子頻帶，5階小波轉換有16個子頻帶等，所以本發明就評估了4、5、6三個不同階層的R-D效能及複雜度。一樣是以lena，大小為512^＊512。 Here, the present invention evaluates how many orders of wavelet transform are used in CS. Because of different wavelet levels, the total number of subbands is also different. For example, the fourth-order wavelet transform has 13 sub-bands, and the fifth-order wavelet transform has 16 sub-bands. Etc. Therefore, the present invention evaluates the RD performance and complexity of three different classes of 4, 5, and 6. The same is in lena, the size is 512 ^* 512.

由第8圖及第9圖所示，可以看到第五階和第六階的R-D效能非常接近，而在計算複雜度方面，可以發現(1)CS編碼器速度遠遠高於CS解碼器(在0.75bpp時編碼器1BCU解碼器為65.22BCU)，(2)bpp越大時編碼時間稍微有增加(1BCU到1.11BCU)，解碼時間減少(65.22到57.91BCU)，(3)小波階數由4變到6得時候，編碼時間增加(1BCU到1.04BCU)，解碼時間則減少(65.22BCU到64.84BCU)，因為6階的計算複雜度比5階多，但是品質不會提升特別高，所以本發明最後決定採用五階段小波轉換。 As shown in Fig. 8 and Fig. 9, it can be seen that the RD performances of the fifth and sixth orders are very close, and in terms of computational complexity, it can be found that (1) the speed of the CS encoder is much higher than that of the CS decoder. (Encoder 1BCU decoder is 65.22BCU at 0.75bpp), (2) The larger the bpp, the larger the encoding time (1BCU to 1.11BCU), the shorter the decoding time (65.22 to 57.91 BCU), and (3) the wavelet order When changing from 4 to 6, the encoding time is increased (1BCU to 1.04BCU), and the decoding time is reduced (65.22BCU to 64.84BCU), because the computational complexity of the 6th order is more than the 5th order, but the quality is not particularly high. Therefore, the present invention finally decided to adopt a five-stage wavelet transform.

四、評估使用DCT或DWT當作CS的稀疏基： 4. Evaluate the use of DCT or DWT as the sparse basis of CS:

DCT和DWT都是兩種常見的稀疏基，那本發明將評估他們的非零係數、非零係數率、平均訊息量、R-D效能及編解碼複雜度，一樣使用lena圖片，大小為512^＊512。 Both DCT and DWT are two common sparse bases, and the present invention will evaluate their non-zero coefficients, non-zero coefficient rates, average message volume, RD performance, and codec complexity, using a lena picture with a size of 512 ^* 512. .

由第10圖可以看到DWT的非零係數及非零係數率都比DCT還要好，也可以發現訊號經過這兩個轉換後所得到的平均訊息量和R-D效能(1)DWT的平均訊息量是4.48bpp而DCT為5.09bpp，(2)從第11圖可以看到DWT的R-D效能優於DCT從1.5db(0.75bpp)到3.2db(1.5bpp)。如第12圖所示，計算複雜度方面DWT的編解碼時間也稍微比DCT還要短一點(編碼1BCU到1.039BCU比上1.20BCU到1.16BCU)，解碼時間也是DWT比DCT還要短一些(59.22BCU到50.16BCU比上58.75BCU到52.11BCU)，所以本發明決定使用DWT來加入往後的研究。 It can be seen from Fig. 10 that the non-zero coefficient and non-zero coefficient rate of DWT are better than DCT, and the average amount of information obtained after the signal is converted by these two signals can also be found. And RD performance (1) The average message volume of DWT is 4.48 bpp and the DCT is 5.09 bpp. (2) From Fig. 11, it can be seen that the RD performance of DWT is better than that of DCT from 1.5 db (0.75 bpp) to 3.2 db (1.5 bpp). ). As shown in Figure 12, the DWT codec time is slightly shorter than the DCT in terms of computational complexity (encoding 1BCU to 1.039BCU compared to 1.20BCU to 1.16BCU), and the decoding time is also shorter than DCT (DWT). 59.22 BCU to 50.16 BCU vs. 58.75 BCU to 52.11 BCU), so the present invention decided to use DWT to join future research.

五、影像編碼利用小波域的性號特性及方向性評估： V. Image coding utilizes the characteristics of the wavelet domain and the directionality evaluation:

在這裡本發明分析CS相關的信號特性，分別是稠密性、稀疏性及均勻性，再來針對小波轉換中HL和LH頻帶係數的方向性進行探討。 Here, the present invention analyzes CS-related signal characteristics, namely, density, sparsity, and uniformity, and then discusses the directionality of HL and LH band coefficients in wavelet transform.

1.稠密性、稀疏性和均勻性 1. Denseness, sparsity and uniformity

在這裡本發明給定N維的稀疏向量(K)為x[n]，n[1,N]，本發明可以定義稠密性D(x)，稀疏性S(x)還有均勻性U(x)： Here, the N-dimensional sparse vector (K) of the present invention is x[n], n [1, N], the present invention can define the density D(x), the sparsity S(x) and the uniformity U(x):

d _i=n _i+1-n _i是分別表示在向量x[n]的非零元素在第i到i+1之間的距離，E(d_i)和U(x)是估測非零元素之間的平均距離。給定一個大小為N的訊號x[n]，較小的K(非零數)就會有較大的稀疏性和較小的稠密性。 d _i = n _{i +1} - n _i are the distances between the i-th and i+1, respectively, of the non-zero elements in the vector x[n], E(d _i ) and U(x) are estimates of non-zero The average distance between elements. Given a signal x[n] of size N, a smaller K (non-zero) will have greater sparsity and less density.

2.小波轉換後的HL/LH頻帶係數的方向性 2. Directionality of HL/LH band coefficients after wavelet transform

LH和HL的子頻帶在經過一階小波轉換分解後的子頻帶方向如第13圖所示者。 The sub-bands of the LH and HL sub-bands are decomposed by the first-order wavelet transform as shown in Fig. 13.

LH的特點是水平方向的頻率會比垂直方向的頻率還高，如第13圖右上角所示，相反HL的特點是垂直方向的頻率會比水平方向的頻率還高，如第13圖左下角所示。因此本發明就研究這兩個頻帶對於CS會不會有更好的效能。在這裡矩陣向量有兩種方法，以水平為主和以垂直為主。 LH is characterized by a higher frequency in the horizontal direction than in the vertical direction, as shown in the upper right corner of Figure 13, whereas HL is characterized by a higher frequency in the vertical direction than in the horizontal direction, as in the lower left corner of Figure 13. Shown. Therefore, the present invention investigates whether these two frequency bands have better performance for CS. There are two methods for matrix vectors here, mainly horizontal and vertical.

第14圖和第15圖是X_LH取水平方向的結果，第16圖和第17圖是X_LH取垂直方向的結果，這裡本發明係針對C_X_LH和R_X_LH的訊號特性分析，包含稀疏性、平均訊息量和均勻性，如第18圖所示。 Figure 14 and Figure 15 show the results of X _{LH in the} horizontal direction, and Figures 16 and 17 show the results of X _{LH in the} vertical direction. The present invention is directed to the analysis of signal characteristics of C_X _LH and R_X _LH , including sparsity. Average message volume and uniformity, as shown in Figure 18.

本發明可以看到(1)兩個的稀疏性和平均訊息量是一樣的，(2)均勻性是C_X_LH比R_X_LH好。那本發明這裡為了改進X的稀疏度，假設門檻值小於5的係數都設為0，在第18圖的After可以看到稀疏度從0.063提高到0.96，E(d_i(X))從1.96升至53.18，這是因為很多系數都變成零的關係(K非零數3837下降至149)。在來比較C_X_LH和R_X_LH在CS的效能，本發明把C_X_LH裡的總個數N_LH=4096分成三個點分別是M_LH=N_LH/2,M_LH=N_LH/4 and M_LH=N_LH/8，來估計bit-rate、平均訊息量還有PSNR。 The present invention can be seen that (1) the sparsity of the two and the average amount of information are the same, and (2) the uniformity is that C_X _{LH is} better than R_X _LH . In order to improve the sparsity of X, it is assumed that the coefficient whose threshold value is less than 5 is set to 0. In the Figure 18, After can see that the sparsity is increased from 0.063 to 0.96, and E(d _i (X)) is from 1.96. It rose to 53.18 because many coefficients became zero (K non-zero 3837 dropped to 149). In C_X _LH and to compare the effectiveness of CS R_X _LH, the present invention is to C_X _LH in the total number N _LH = 4096 points are divided into three _{_{M LH = N LH / 2,}} M LH = N LH / 4 and M _LH = N _LH /8 to estimate bit-rate, average message volume, and PSNR.

第19圖和第20圖是C_X_LH和R_X_LH的R-D效能圖及數據表，可以發現C_X_LH的R-D效能比R_X_LH的還要好，以上面這樣分析來說，本發明可以推斷在HL頻帶，R_X_HL的均勻性和R-D效能應該都會比C_X_HL還要好。 Figure 19 and Figure 20 is c_x R_X _LH and _LH potency of FIG RD and a data table can be found in the RD c_x _LH _LH potency even better than R_X, such the above analysis, the present invention can be deduced in the HL band, R_X _HL RD uniformity and effectiveness will be even better than c_X _HL.

步驟(c).各頻帶分別進行純量量化： Step (c). Each frequency band is separately scalar quantized:

一、將JND量化於小波次頻帶： 1. Quantify the JND to the wavelet sub-band:

本發明係為在編碼中加入量化可以有效改進R-D效能，舉例來說像JPEG(Joint Picture Expert Group)影像壓縮標準有採用8^＊8量化表來改進R-D效能。每一個8^＊8DCT係數都有對應的量化表，這個量化表示依照人類視覺所產生的。一般情況下，在比較低頻係數，人類的視覺會比較敏感，在比較高頻的係數，相對比較不敏感。因此本發明將小波編碼原影像分解成若干的次頻帶，每個次頻帶的JND_threshold的計算方法如下：其中u，v：honzontal & vertical frequency vespectively.JND _sb,ori(u,v)的意義是：次頻帶(sb)在frequency domain中的每一個頻率(u,v) sb計算出其綜合頻率，而由頻率JND曲線JND _ori(f)所對應之JND值。JND_threshold Γ_sb可視為在該次頻帶各頻率JND值的方均根(mean square root)，各個subband的JND_threshold基本上只與人眼特性有關而不受影像特性所影響。表3.6為上述公式計算出各次頻帶之JND_threshold，可以依據JND_threshold把不重要(insignificant)的係數捨去。所謂的捨去就是把絕對值小於JND_threshold的係數量化為零，最後本發明採用該次頻帶每個頻率所對應的JND值之均方根值為本發明的JND_threshold，如第21圖所示者。 The present invention is effective for improving RD performance by adding quantization to the encoding. For example, the JPEG (Joint Picture Expert Group) image compression standard has an 8 ^* 8 quantization table to improve the RD performance. Each 8 ^* 8 DCT coefficient has a corresponding quantization table, which is generated in accordance with human vision. In general, in comparing the low-frequency coefficients, human vision will be more sensitive, and relatively high-frequency coefficients are relatively insensitive. Therefore, the present invention decomposes the wavelet-encoded original image into a plurality of sub-bands, and the JND_threshold of each sub-band is calculated as follows: Where u, v:honzontal & vertical frequency vespectively.JND _{sb , ori} ( u , v ) means: each frequency ( u , v ) of the sub-band (sb) in the frequency domain Sb calculates its comprehensive frequency And the JND value corresponding to the frequency JND curve JND _ori ( f ). JND_threshold Γ _sb can be regarded as the mean square root of the JND value of each frequency in the sub-band, and the JND_threshold of each subband is basically only related to the characteristics of the human eye and is not affected by the image characteristics. Table 3.6 calculates the JND_threshold for each frequency band for the above formula, and can discard the coefficient of insignificant according to JND_threshold. The so-called rounding is to quantize the coefficient whose absolute value is smaller than JND_threshold to zero. Finally, the rms value of the JND value corresponding to each frequency of the subband is used in the present invention as the JND_threshold of the present invention, as shown in FIG.

步驟(d).計算各頻帶的非零係數比並分配各次頻帶權重： Step (d). Calculate the non-zero coefficient ratio of each frequency band and assign each sub-band weight:

一、量測向量之FLC與VLC性能評估： First, the measurement vector FLC and VLC performance evaluation:

因為過去做法是用Entropy來估計Bit_Rate，而本發明為了更接近實際情況，所以在量測向量後加入了實際編碼狀況，並且比較加入FLC與VLC，目前已知VLC的效果一定會比FLC還要好，但是複雜度會增加，那如果經過VLC後的R-D曲線優勢比FLC還要大很多，就會採用VLC來當作量測向量後的處理。 Because the past practice is to use Entropy to estimate Bit_Rate, and in order to get closer to the actual situation, the actual coding condition is added after the measurement vector, and the FLC and VLC are added. The effect of VLC is known to be better than FLC. However, the complexity will increase. If the advantage of the RD curve after VLC is much larger than that of FLC, VLC will be used as the processing after the measurement vector.

(一)、對於Y _M×1後面加入FLC的位元率評估步驟：FLC(Fixed Length Coding)固定長度編碼是N個符號symbol，每個符號用固定log₂ N個bits表示。詳細步驟如下： (1) For the bit rate evaluation step of adding FLC after Y _{M ×1} : FLC (Fixed Length Coding) fixed length coding is N symbol symbols, and each symbol is represented by a fixed log ₂ N bits. The detailed steps are as follows:

1.求輸出量測向量Y_M×1={y₁,y₂,……y_M}^T的係數： 1. Find the output measurement vector Y _{M × 1} = {y ₁ , y ₂ , ... y _M } ^T coefficient:

這邊本發明將Y_M×1裡的M個係數都先round(四捨五入)到整數位，向量Y_M×1中共有N個不同係數值，N=Y_max-Y_min+1其中Y_max及Y_min分別為Y_M×1的最大值和最小值，不同影像的Y_M×1其最大值和最小值也會有所不同。 In the present invention, the M coefficients in Y _M×1 are rounded (rounded) to integer bits, and there are N different coefficient values in the vector Y _M×1 , N=Y _max −Y _min +1 where Y _max and Y _min are the maximum and minimum Y _{M × 1,} except the image Y _{M × 1} its maximum and minimum values will vary.

2.計算出向量Y_M×1的bit數Y_bit。公式為Y_bit=ceil(log₂ N)N>0,ceil：無條件進位，單位：bit (式4.1) Ex.ceil(log₂ 6)=3 Y_bit=3 2. Calculate the number of bits Y_bit of the vector Y _{M × 1} . The formula is Y _bit =ceil(log ₂ N)N>0, ceil : unconditional carry, unit: bit (formula 4.1) Ex.ceil(log ₂ 6)=3 Y_bit=3

3.計算位元率Bit rate(bpp,bits per pixel)。公式為 3. Calculate the bit rate (bpp, bits per pixel). Formula is

(二)、對於Y _M×1後面加入VLC的位元率評估步驟：VLC(Variable Length Coding)可變長度編碼是將資料中出現機率較低之符號以較長位元的字碼來編碼；而出現機率較高之符號則是用較短位元的字碼來編碼，這樣的好處是，可以在編碼同時也達到資料壓縮的效果，其中霍夫曼編碼是非常逼近entropy的，所以本發明選擇使用霍夫曼編碼來加入本發明的架構中。使用的霍夫曼程式是數位影像處理-運用MATLAB課本裡面的toolbox。詳細步驟如下： (2) For the bit rate evaluation step of adding VLC after Y _{M ×1} : VLC (Variable Length Coding) variable length coding is to encode a symbol with a lower probability in the data with a longer bit code; The symbol with higher probability is encoded by the code of the shorter bit. This has the advantage that the data compression effect can be achieved at the same time, and the Huffman coding is very close to the entropy, so the invention chooses to use Huffman coding is incorporated into the architecture of the present invention. The Huffman program used is digital image processing - using the toolbox in the MATLAB textbook. The detailed steps are as follows:

1.把原本量測向量Y_M×1先round(四捨五入)到整數位，表示為Y_M×1=round(Y_M×1) (式4.3) 1. The original measurement vector Y _{M×1 is} rounded (rounded) to an integer number, expressed as Y _M×1 =round(Y _M×1 ) (Equation 4.3)

2.經過霍夫曼編碼後會得到新的資料量，表示為huff_Y_M=mat2huff(Y_M×1) (式4.4) 2. After Huffman coding, a new amount of data will be obtained, expressed as huff_Y _M = mat2huff(Y _M×1 ) (Equation 4.4)

4.計算Y_M×1經過霍夫曼之後的平均編碼長度 4. Calculate the average code length after Y _M×1 after Huffman

(三)、對於Y _M×1的Entropy計算 (III) Entropy calculation for Y _{M ×1}

1.求輸出量測向量Y_M×1={y₁,y₂,……y_M}^T 1. Find the output measurement vector Y _{M × 1} = {y ₁ , y ₂ , ... y _M } ^T

機率分佈(histogram)：這邊本發明一樣將Y_M×1裡的M個係數都先round(四捨五入)到整數位，向量Y_M×1中共有N個不同係數值，N=Y_max-Y_min+1其中Y_max及Y_min分別為Y_M×1的最大值和最小值，不同影像的Y_M×1其最大值和最小值也會有所不同，這時候Y_M×1量測向量的機率分佈histogram其中n_k是第k個係數k{1,2,...,N}出現在Y_M×1的次數。 Histogram: Here, in the present invention, the M coefficients in Y _M×1 are rounded (rounded) to integer bits, and there are N different coefficient values in the vector Y _M×1 , N=Y _max -Y _min +1 wherein Y _max and Y _min are the maximum and minimum Y _{M × 1,} except the image Y _{M × 1} its maximum and minimum values will be different, this time measurement Y _{M × 1} vector Probability distribution histogram Where n _k is the kth coefficient k {1,2,...,N} The number of times Y _M×1 appears.

2.計算出Y_M×1的entropy。公式為 2. Calculate the entropy of Y _{M × 1} . Formula is

(四)評估其效能及複雜度的估計： (d) Estimating the effectiveness and complexity of the estimate:

在這裡是用PSNR vs.Bit Rate當作效能評估，複雜度則是用時間來估計，測試環境是在沒有執行其他應用程式與其他干擾下執行。執行程式時，加入FLC及加入VLC是分開進行的。測試圖片是用lena、peppers、boat、baboon為樣本如第22圖所示，其解析度大小為512^＊512灰階，檔案格式為bmp。Measurment_Rate則是使用0.1、0.15、0.2、0.25、0.3來當作同一品質下的固定參數，並會得到不同的Bit rate來做比較。程式所執行的時間，分為編碼及解碼，所使用實驗設備如第第23圖所示。 Here, PSNR vs. Bit Rate is used as the performance evaluation, and complexity is estimated by time. The test environment is executed without executing other applications and other interference. When the program is executed, joining the FLC and joining the VLC are performed separately. The test picture is a sample of Lena, Peppers, boat, and baboon as shown in Figure 22. The resolution is 512 ^* 512 grayscale and the file format is bmp. Measurment_Rate uses 0.1, 0.15, 0.2, 0.25, and 0.3 as fixed parameters of the same quality, and will get different Bit rates for comparison. The time that the program executes is divided into encoding and decoding. The experimental equipment used is shown in Figure 23.

以PSNR vs.Bit Rate實驗結果第24圖到第27圖來看，以第24圖lena來說，x軸表示Bit_Rate，y軸表示PSNR，取最低點的座標VLC(0.43,23.33)、FLC(0.8,23.35)來看，當MR固定在0.1的時候Bit_Rate分別為0.43bpp和0.8bpp，PSNR分別為23.33db及23.35db，可以發現(1)固定MR，但是PSNR不會一樣，因為他是以隨機取樣的方式進行，所以固定MR所得到品質會很接近(PSNR不會差超過0.2db)，(2)VLC可變長度編碼所需要的Bit_Rate比FLC固定長度編碼少很多，最多可以少1.13bpp(第24圖，1.27bpp和2.4bpp的差值)，(3)如果以Bit_Rate大約為1.2bpp來看，VLC所得到的品質大約比32.06db在一低點，FLC所得到的品質25.82db，兩者相差大約6.26db，(4)也可以發現曲線開口會隨MR越高，開口越高。 Taking the PSNR vs. Bit Rate results from Fig. 24 to Fig. 27, in the case of Lena in Fig. 24, the x-axis represents Bit_Rate, the y-axis represents PSNR, and the coordinates of the lowest point are VLC (0.43, 23.33), FLC ( 0.8, 23.35), when the MR is fixed at 0.1, the Bit_Rate is 0.43bpp and 0.8bpp respectively, and the PSNR is 23.33db and 23.35db respectively. It can be found that (1) fixed MR, but the PSNR will not be the same, because he is Random sampling, so the quality of fixed MR will be very close (PSNR will not exceed more than 0.2db), (2) Bit_Rate required for VLC variable length coding is much less than FLC fixed length coding, up to 1.13 Bpp (Fig. 24, the difference between 1.27bpp and 2.4bpp), (3) If the Bit_Rate is about 1.2bpp, the quality obtained by VLC is about a low point than 32.06db, and the quality obtained by FLC is 25.82db. The difference between the two is about 6.26 db. (4) It can also be found that the higher the opening of the curve, the higher the opening.

以時間來估計複雜度的第28圖到第31圖來看，以第28圖leana來說，當MR從0.1調整到0.3時，FLC編碼時間從0.26s增加至0.27s，VLC編碼時間從0.33s增加至0.42s，如果換算就是27%增加到56%，可以發現VLC可變長度編碼所花的編碼時間都比FLC固定長度編碼所花的編碼時間還多，最多是增加56%(如表3.4，MR=0.3)的時間。 Looking at the 28th to 31st graphs of the time to estimate the complexity, in the case of leana in Fig. 28, when the MR is adjusted from 0.1 to 0.3, the FLC encoding time is increased from 0.26s to 0.27s, and the VLC encoding time is from 0.33. s increased to 0.42s, if the conversion is 27% increased to 56%, it can be found that VLC variable length coding takes more coding time than FLC fixed length coding, up to 56% (such as 3.4, MR = 0.3) time.

最後第32圖到第35圖是說明本發明所使用的霍夫曼編碼所得到的bit數和Entropy是非常接近的，以第32圖lena來說，MR從0.1增加至0.3，Entropy和Huff_avg最少差0.03，最多差0.04，也間接說明本發明所使用的霍夫曼編碼程式的可靠度。 Finally, Fig. 32 to Fig. 35 are diagrams showing that the number of bits obtained by the Huffman coding used in the present invention is very close to Entropy. In the case of Len in Fig. 32, MR is increased from 0.1 to 0.3, and Entropy and Huff_avg are the least. The difference is 0.03, and the difference is 0.04 at the most, which also indirectly illustrates the reliability of the Huffman coding program used in the present invention.

(五).Y _M×1在VLC時分開處理： (V). Y _M×1 is treated separately at VLC:

在Y_M×1裡面有LL、HL、LH、HH四個band的所有係數，在VLC的時候，因為是利用機率分佈來編碼，四個band裡面每個band的係數都有相關性，所以本發明在這裡把四個band分別做VLC之後再做傳送，合起來架構如第36圖，分開的架構圖是第37圖。這樣做複雜度可能會增加，但是總bits數會變少，最後將由實驗結果來評估是否將四個band分別做VLC。 In Y _M×1, there are all coefficients of LL, HL, LH, and HH. In VLC, because the probability distribution is used, the coefficients of each band in the four bands are related, so this The invention here transmits the four bands separately after VLC, and the combined architecture is as shown in Fig. 36, and the separate architecture diagram is Fig. 37. The complexity may increase, but the total number of bits will decrease. Finally, the experimental results will be used to evaluate whether the four bands are VLC.

從第38圖所示者係表示四個band一起做VLC及分開做VLC的總bits數比較，可以發現總bits數都是減少的狀態，其中減少最多的為表4.14，MR等於0.3時，兩個相差57808個bits數；第39圖及第40圖所示者係時間複雜度的比較，可以發現時間上沒有大幅上升很多。從以上實驗結果，本發明決定使用四個band分別做VLC可變長度編碼來加入本發明的架構中，當作往後各步驟的基準。 From the figure shown in Figure 38, the total number of bits of VLC and VLC are compared. It can be found that the total number of bits is reduced. The most significant reduction is shown in Table 4.14. When MR is equal to 0.3, two The difference is 57808 bits; the comparison of the time complexity shown in Fig. 39 and Fig. 40 shows that there is not a significant increase in time. From the above experimental results, the present invention decided to use four bands for VLC variable length coding to join the architecture of the present invention as a reference for the subsequent steps.

二、小波轉換各頻帶的CS特性分析 Second, the analysis of CS characteristics of each frequency band of wavelet transform

壓縮取樣的基本假設是信號具有稀疏性(SPARSITY)，而小波轉換後的各次頻帶經個別JND量化後的稀疏程度都有所不同，直覺上去推論量測率MR分配應與SPARSITY成反比，因稀疏度越高，帶訊息的非零係數越少，其訊息量(ENTROPY)較低、故其MR或Bit_Rate(BR)應相對較小。本節目的是探討各次頻帶稀疏性與訊息量的關係，並據以分配各次頻帶適當之MR及BR。 The basic assumption of compressed sampling is that the signal has sparsity (SPARSITY), and the sparseness of each sub-band after wavelet transform is different after quantification by individual JND. Intuitively, the inferential measurement rate MR allocation should be inversely proportional to SPARSITY. The higher the sparsity, the less the non-zero coefficient with the message, and the lower the message volume (ENTROPY), so its MR or Bit_Rate(BR) should be relatively small. This program is to explore the relationship between the sparseness of each frequency band and the amount of information, and to allocate appropriate MR and BR for each sub-band.

1.各次頻帶的CS特性分析 1. Analysis of CS characteristics of each frequency band

各個band因為特性不同，所以非零係數所佔的比例也不一樣，這邊以來代表，K表示非零的個數，N表示該頻帶的總係數，K的數量越多就越不稀疏，因此定義稀疏性，S越大代表非零係數越少即稀疏性高。下面有lena、peppers、boat、baboon四張圖片，檔案格式為bmp檔，大小為512^＊512，各個不同band 的稀疏性SPARSITY及ENTROPY分析。 Because each band has different characteristics, the proportion of non-zero coefficients is different. To represent, K represents the number of non-zero, N represents the total coefficient of the frequency band, and the more the number of K, the less sparse, so the definition of sparsity The larger S, the less the non-zero coefficient is, the higher the sparsity. Below are four pictures of lena, peppers, boat, baboon, the file format is bmp file, the size is 512 ^* 512, sparse SPARSITY and ENTROPY analysis of different bands.

第41圖及第42圖分別是lena、peppers、boat、baboon四張圖片各個band的稀疏性與訊息量，可以發現越高頻帶稀疏程度越高，而越低頻帶稀疏程度越低，也可以發現越稀疏的時候，Entropy也越小。根據這樣的結果，下面一章，會探討利用稀疏度延伸出非零係數比的觀點。 Figure 41 and Figure 42 show the sparseness and amount of each band of the four pictures of lena, peppers, boat, and baboon. It can be found that the higher the frequency band sparseness, the lower the band sparsity is, the lower the frequency can be found. The thinner the Entropy, the smaller. Based on this result, the following chapter will explore the idea of using sparsity to extend the non-zero coefficient ratio.

三、使用非零個數比例來分配次頻帶權重： Third, use a non-zero number ratio to allocate sub-band weights:

1.非零個數比例來分配次頻帶權重動機 1. Non-zero number ratios to assign sub-band weighting motives

本發明方法若以初步分配量測率，分配後的品質比原先的好。本發明係進一步的由第41圖及第42圖的各band的CS特性分析，可以發現越低頻帶稀疏度越低，ENTROPY越高，這也表示，非零的個數相對越多，因此本發明將藉由各個band非零個數的關係，來做為量測率分配的基準。 If the method of the present invention preliminarily allocates the measurement rate, the quality after the distribution is better than the original one. According to the CS characteristic analysis of each of the bands of FIG. 41 and FIG. 42, it can be found that the lower the band sparsity, the higher the ENTROPY, which means that the number of non-zero is relatively large, so The invention will use the relationship of the non-zero numbers of the bands as the basis for the measurement rate allocation.

2.介紹非零個數及非零係數比 2. Introduce non-zero numbers and non-zero coefficient ratios

以第41圖lena的LL5頻帶來看，LL5的大小為256，稀疏度是0，以HH1頻帶來看，HH1的大小是256^＊256，稀疏度是0.9999，可以發現越低頻帶，所占的非零個數越多，稀疏度也就越低，重要資訊也都集中在低頻帶，高頻帶的地方所占的非零個數也就較少，相對就很稀疏，資訊的重要性也比較低。 Looking at the LL5 band of the lens of Fig. 41, the size of LL5 is 256, and the sparsity is 0. In the HH1 band, the size of HH1 is 256 ^* 256, and the sparsity is 0.9999. The lower the frequency band can be found. The more non-zero numbers, the lower the sparsity, the more important information is concentrated in the low frequency band, the non-zero number in the high-band area is less, the relative is very sparse, and the importance of information is also compared. low.

因此本發明定義非零係數比，簡稱NZR(non-zero-ratio)，一張圖片經過小波轉換及量化後的的非零係數比(NZR)等於各個頻帶的非零個數(non_zero_band)除以全部頻帶的非零個數總合 (total_non_zero)，以計算LL5的非零係數比為例，LL5的非零係數比公式為藉由式4.8將所有band的非零個數比(NZR)求出來，如第43圖及第44圖所示者。 Therefore, the present invention defines a non-zero coefficient ratio, referred to as NZR (non-zero-ratio), the non-zero coefficient ratio (NZR) of a picture after wavelet transform and quantization is equal to the non-zero number of each frequency band (non_zero_band) divided by For the total number of non-zero numbers of all frequency bands (total_non_zero), to calculate the non-zero coefficient ratio of LL5, the non-zero coefficient ratio formula of LL5 is The non-zero number ratio (NZR) of all bands is obtained by Equation 4.8, as shown in Figs. 43 and 44.

如此可以觀察到baboon這張圖片因為是屬於高頻訊號較多，所以總非零個數非比其他圖片的非零個數還要多很多，因此在低頻帶的非零係數比，會相對比其他圖片還小，而在高頻帶的非零係數比也比其他圖片還大。 So you can observe that this picture of baboon is because there are more high-frequency signals, so the total non-zero number is not much more than the non-zero number of other pictures, so the ratio of non-zero coefficients in the low frequency band will be relatively Other pictures are still small, and the non-zero coefficient ratio in the high frequency band is also larger than other pictures.

3.使用非零係數比分配次頻帶權重的方法及步驟 3. Methods and steps for assigning sub-band weights using non-zero coefficient ratios

上述介紹了非零係數比，在這裡本發明將非零係數比加入壓縮感測的量測率權重分配，之前由本實驗室提出初步分配，是將五階小波轉換，分成四個頻帶去做處理，那本發明這裡討論了各頻帶的非零係數比，以這些非零係數比當作量測率權重分配，因此本發明將五階小波轉換的各頻帶，分別經過量化後，分成十六個頻帶去做壓縮感測處理其編碼及解碼流程如第45圖、第46圖所示者。 The above describes a non-zero coefficient ratio. Here, the present invention assigns a non-zero coefficient ratio to the measurement rate weight of the compression sensing. Previously, the laboratory proposed a preliminary allocation, which is to convert the fifth-order wavelet into four frequency bands for processing. The invention herein discusses the non-zero coefficient ratio of each frequency band, and these non-zero coefficient ratios are assigned as the measurement rate weights. Therefore, the present invention divides the frequency bands of the fifth-order wavelet transform into sixteen respectively. The frequency band is subjected to compression sensing processing, and the encoding and decoding processes are as shown in Figs. 45 and 46.

四、本步驟會遭遇到的困難與其解決辦法： Fourth, the difficulties encountered in this step and its solutions:

本節係以John Hopkins University Thong Do所提供的壓縮取樣架構下，來執行本發明的實驗。 This section performs the experiments of the present invention under the compression sampling architecture provided by John Hopkins University Thong Do.

1.所遭遇的困難 1. The difficulties encountered

困難1，如果MR小於某個值，會發生影像沒辦重建回來，PSNR值變成負的造成重建失敗(程式可執行)，第47圖為boat在MR=0.1時，所重建回來的圖片。本發明發現連boat的外型都無法產生，這個原因可能是給的MR太低，導致總取樣個數太少，所以沒辦法將圖片完整重建回來。 Difficulty 1. If MR is less than a certain value, the image will not be reconstructed, the PSNR value will become negative, and the reconstruction will fail (program executable). Figure 47 shows the reconstructed picture when the boat is MR=0.1. The invention finds that even the appearance of the boat cannot be produced. The reason may be that the MR is too low, resulting in too few total samples, so there is no way to completely reconstruct the picture.

困難2，如果HH1向量內的值全部未滿0.5會造成HH1無法執行GPSR重建工作(程式無法執行完成)。當本發明執行壓縮感測後，會先進行round處理，讓他四捨五入到整數，才進行huffman編碼，因為在huffman編碼時，是依原始訊源符號出現機率由大到小排序，這個過程會一直重複直到訊源碼只剩下兩個符號為止，所以如果不進行整數化的動作，會使這個過程消耗大量時間。因為執行round這個動作，使的未滿0.5的數都會變成0，如果HH1裡面的值全部都變為0，解碼時沒有資料可以重建回來，就會造成HH1無法執行GPSR重建工作，所以本發明的解決辦法是當HH1全部的值都未滿0.5就捨棄HH1。 Difficulty 2, if the values in the HH1 vector are all less than 0.5, HH1 cannot perform GPSR reconstruction (the program cannot be completed). When the present invention performs compression sensing, it will perform round processing first, and then round it to an integer to perform huffman coding, because in huffman coding, the probability of occurrence of the original source symbols is ranked from large to small, and the process will always be Repeat until the source code has only two symbols left, so if you do not perform integer operations, this process will consume a lot of time. Because the round action is performed, the number of less than 0.5 will become 0. If the values in HH1 all become 0, no data can be reconstructed when decoding, which will cause HH1 to perform GPSR reconstruction, so the present invention The solution is to discard HH1 when all HH1 values are less than 0.5.

困難3，如果MR大於某個值，會發生無法執行此程式，以lena 512×512圖片的LL5做說明，LL5的解析度為16×16，NZR_LL5=0.0056(LL5的非零係數比)，因此NZR_LL5×M=0.0056×512×512×MR，如果MR太大會造成NZR_LL5×M>16×16，也就是超過LL5頻帶解析度的大小，造成無法執行此程式。當給定的MR值會使NZR_band×M>band_size，會變成取樣總數大於等於原本該頻帶的大小，造成沒有意義的行為，所以本發明的解決辦法就是直接讓他傳送不做壓縮感測。 Difficulty 3, if the MR is greater than a certain value, the program cannot be executed. The LL5 of the lena 512×512 picture is explained. The resolution of LL5 is 16×16, NZR_LL5=0.0056 (the non-zero coefficient ratio of LL5), so NZR_LL5×M=0.0056×512×512×MR. If the MR is too large, it will cause NZR_LL5×M>16×16, which is the size of the LL5 band resolution, which makes it impossible to execute this program. When a given MR value causes NZR_band×M>band_size, it will become the total number of samples greater than or equal to the size of the original band, causing meaningless behavior, so The solution of the invention is to let him transmit directly without compression sensing.

2.解決辦法 2. Solution

困難1的解決辦法，在最後計算完PSNR的地方加入第一判別式，如果PSNR小於零，代表重建失敗，因此本發明把MR值進行累加的動作，然後重新執行程式，直到PSNR大於零才進行輸出的動作，如第48圖所示者。 In the solution of difficulty 1, the first discriminant is added where the PSNR is finally calculated. If the PSNR is less than zero, it represents the reconstruction failure. Therefore, the present invention accumulates the MR value and then re-executes the program until the PSNR is greater than zero. The output action is as shown in Figure 48.

困難2的解決辦法，加入第二判別式，當HH1經過壓縮感測後所得到的向量，針對此向量去進行掃描，如果全部的值都未滿0.5，則捨棄HH1，在解碼時用相同大小的零矩陣來代替HH1，如果原本HH1有值大於等於0.5就依照原本流程走，如第49、50圖所示者。 In the solution of difficulty 2, the second discriminant is added. When the vector obtained by HH1 is subjected to compression sensing, the vector is scanned. If all the values are less than 0.5, HH1 is discarded, and the same size is used in decoding. The zero matrix replaces HH1. If the original HH1 has a value greater than or equal to 0.5, it follows the original flow, as shown in Figures 49 and 50.

困難3的解決方法，加入第三判別式，在輸入固定MR之後，每個band要做壓縮感測前進行判別，如果NZR_band×M>band_size的話，就讓該頻帶直接傳送到VLC編碼，不做壓縮感測，如果NZR_band×M<band_size就依照原本流程走，如第49、50圖所示者。 For the solution of difficulty 3, the third discriminant is added. After inputting the fixed MR, each band is subjected to compression sensing for discrimination. If NZR_band×M>band_size, the band is directly transmitted to the VLC code, and no Compressed sensing, if NZR_band×M<band_size follows the original flow, as shown in Figures 49 and 50.

實驗的測試平台軟硬體規格都如第23圖所示者，在這裡是用PSNR vs.Bit Rate當作效能評估，以時間當作複雜度評估，測試環境是在沒有執行其他應用程式與其他干擾下執行。測試圖片是用lena、peppers、boat、baboon為樣本，檔案格式為bmp檔，其解析度大小為512^＊512灰階。Measurment_Rate則是依照圖片不同而設定不同的值，lena分別是0.11、0.14、0.17，baboon分別是0.39、 0.42、0.45，boat分別是0.18、0.21、0.24，peppers分別是0.12、0.15、0.18，由十六個頻帶分開做壓縮感測加上非零個數比例分配次頻帶權重和次頻帶全部合起來做一次壓縮感測全部隨機分配來做比較。 The experimental software platform hardware and software specifications are as shown in Figure 23. Here, PSNR vs. Bit Rate is used as the performance evaluation, and time is used as the complexity evaluation. The test environment is not executing other applications and other. Execute under interference. The test picture is a sample of lena, peppers, boat, baboon, and the file format is bmp file, and its resolution is 512 ^* 512 gray scale. Measurment_Rate sets different values according to different pictures, lena is 0.11, 0.14, 0.17, baboon is 0.39, 0.42, 0.45, boat is 0.18, 0.21, 0.24, respectively, and pepperers are 0.12, 0.15, 0.18, respectively. The six frequency bands are separately compressed and the non-zero number ratios are allocated. The sub-band weights and the sub-bands are all combined to make a compression sensing all randomly assigned for comparison.

第51圖至第52圖係為四張圖片非零個數比例分配權重和全部隨機分配的R-D曲線，接著來看第53圖的時間複雜度。 Fig. 51 to Fig. 52 are four picture non-zero number distribution weights and all randomly assigned R-D curves, and then the time complexity of Fig. 53 is seen.

第51圖的lena512^＊512非零個數比例分配權重和全部隨機分配可以觀察到，隨機分配在大約0.53bpp的時候，品質大約是18.12db，而藉由非零個數比例來分配各頻帶權重所得到的結果，在0.55bpp的時候，品質可以遠遠超出全部隨機分配大約12db，來到30.17db，可以看到在同一bpp下雖然複雜度增加，但是品質有驚人的提升，其他三張圖片也顯示出，使用非零個數比例分配次頻帶權重效果大大的提升。在這裡可以觀察到每張圖片所給的MR的範圍有所不同，尤其是baboon這張圖片，最低能重建的MR值需要到0.39，本發明也針對這樣的結果來觀察是否和其他數據有關係，進而發現到baboon的非零個數是四張圖片中最多的，也代表說，在低頻帶的非零係數比相較於另外三張圖片會是偏低的狀態，因此在重建的時候如果一開始給的MR值太低，也就是總取樣數太少，就會發生重建失敗的現象，另外也發現除了baboon以外的圖片，HH1都是用零矩陣取代，也就是說明大部分圖片的HH1可能都是如此。 The lena512 ^* 512 non-zero number distribution weight and all random allocations in Fig. 51 can be observed. When the random allocation is about 0.53bpp, the quality is about 18.12db, and the weight of each band is allocated by the non-zero number ratio. The result obtained, at 0.55bpp, the quality can be far beyond the random allocation of about 12db, to 30.17db, you can see that although the complexity increases under the same bpp, but the quality is amazingly improved, the other three pictures It has also been shown that the effect of assigning sub-band weights using a non-zero number ratio is greatly improved. Here, we can observe that the range of MR given by each picture is different. Especially for the picture of baboon, the minimum reconstructable MR value needs to be 0.39. The present invention also observes whether the result is related to other data. And found that the non-zero number of baboon is the largest of the four pictures, which also means that the non-zero coefficient in the low frequency band will be lower than the other three pictures, so if it is reconstructed The MR value given at the beginning is too low, that is, the total number of samples is too small, and the reconstruction failure will occur. In addition, the pictures other than baboon are found, HH1 is replaced by a zero matrix, that is, the HH1 of most pictures is shown. This may be the case.

五、各頻帶分別不經過壓縮感測處理的品質評估： 5. Quality assessment of each frequency band without compression sensing:

因為CS的理論是適用於稀疏訊號，對於低頻次頻帶而言，若分配到的MR較高時，次頻帶所有係數做直接傳送的效果可能比經過CS還要好，因此本發明這節評估各頻帶如果不經過CS_Wavelet而直接傳送的效果會是如何。 Since the theory of CS is applicable to sparse signals, for low-frequency sub-bands, if the assigned MR is higher, the effect of direct transmission of all coefficients of the sub-band may be better than that of CS, so the present invention evaluates each band. What if the effect of direct transmission without CS_Wavelet?

在第49圖所示的流程圖，進行壓縮感測前，都會進行判斷，而本發明這邊是不用判斷，直接把其中幾個的band不經過壓縮感測直接做傳送的動作。這邊本發明分成A、B、C、D、E五種CASE，如第54圖所示者。 In the flowchart shown in Fig. 49, before the compression sensing is performed, the judgment is made, and the present invention does not need to judge, and directly transmits the bands of several of them without compression sensing. Here, the present invention is divided into five CASEs of A, B, C, D, and E, as shown in Fig. 54.

另外要注意的地方是，在不同曲線，總取樣各數和總非零個數都要扣掉一些，舉例來說，再計算M的時侯，原本是圖片解析度假設是lena512^＊512，那麼M=512×512×MR，但是如果要計算CASE_D的時候必須要把不做壓縮感測範圍的大小扣掉，CASE_D不做壓縮感測的範圍是Lv5(LL5到HH5)，也就是32^＊32的範圍，因此計算M的時候要扣掉32^＊32變成M=(512×512-32×32)×MR。 Another point to note is that in different curves, the total number of samples and the total number of non-zero numbers must be deducted. For example, when calculating M again, the original picture resolution is assumed to be lena512 ^* 512, then M=512×512×MR, but if you want to calculate CASE_D, you must deduct the size of the compression sensing range. The range of CASE_D without compression sensing is Lv5 (LL5 to HH5), which is 32 ^* 32. The range, so when calculating M, deduct 32 ^* 32 into M = (512 × 512 - 32 × 32) × MR.

計算非零係數比時，分母也要跟著扣掉不做壓縮感測範圍內的各頻帶非零個數的和，也就代表如果是要算全不經過CS的lena LH4的，原本就依照定義但是如果到Case_D的話因為Lv5不做壓縮感測，所以公式變成針對不同的狀況，就扣掉不同的範圍。 When calculating the non-zero coefficient ratio, the denominator should also be deducted from the sum of the non-zero numbers of the frequency bands in the compression sensing range, which means that if it is to calculate the lena LH4 without CS, it is originally defined. However, if you go to Case_D, because Lv5 does not perform compression sensing, the formula becomes Different ranges are deducted for different situations.

一樣是選用四張圖片，分別是lena、peppers、boat、baboon，解析度大小都為512^＊512，這邊的實驗結果共分成8種CASE，8種CASE的說明，如第55圖所示者。 The same four images are selected, which are lena, peppers, boat, baboon, and the resolution is 512 ^* 512. The experimental results here are divided into 8 kinds of CASE, 8 kinds of CASE instructions, as shown in Figure 55. .

一樣是選用四張圖片，分別是lena、peppers、boat、baboon，解析度大小都為512^＊512，這邊的實驗結果共分成8種CASE，8種CASE的說明，如第56圖所示者。 The same four images are selected, which are lena, peppers, boat, baboon, and the resolution is 512 ^* 512. The experimental results here are divided into 8 kinds of CASE, 8 kinds of CASE instructions, as shown in Figure 56. .

由第56圖至第59圖來看，發現(1)CASE_A到CASE_E最左邊的點是MR等於零，也就是A、B、C、D、E這五種CASE有固定的頻帶做直接傳送，代表有一定的資訊量傳送到解碼端去做解碼的動作，因此在MR可以由零開始，(2)另外F、G、H這三種CASE，因為沒有固定的頻帶做直接傳送的動作，因此會發生困難2，也就是MR等於零的時候無法執行壓縮感測，也就代表解碼端沒有資訊可以做重建，(3)CASE_A到CASE_H的MR值都可以到0.99，除了CASE_G不行以外，因為CASE_G是初步分配，沒有加入判別式，所以在MR大於等於0.5的時候，就會發生困難3，也就是總取樣數就會大於其解析度大小，因此無法執行壓縮感測，圖片上也就無法顯示了，(4)CASE_A在MR等於零時，因為是頻帶LL5到頻帶HH2做直接傳送的動作，所以起始的bpp就會偏高，品質也會較好，(5)當MR越高也就是bpp越高時，因為判別式NZR_band×M>band_size都會成立，所以頻帶都不會經過壓縮感測，因此CASE_A到CASE_F的曲線就會越來越趨近於某個值。因為baboon是屬於高頻訊號較多的一張圖片，在一般比較不常見，因此對此圖片先不做探討，四張圖片的CASE_H曲線(隨機分配)，因為在MR=0.5及0.99，Bit_Rate都很大但是品質最多到33db而已，所以H曲線就沒有完整的呈現。 From Fig. 56 to Fig. 59, it is found that (1) the leftmost point of CASE_A to CASE_E is MR equal to zero, that is, the five CASEs of A, B, C, D, and E have fixed frequency bands for direct transmission, representing There is a certain amount of information transmitted to the decoding end for decoding, so the MR can start from zero, and (2) the other three CASEs of F, G, and H, because there is no fixed frequency band for direct transmission, so it will happen. Difficult 2, that is, when MR is equal to zero, compression sensing cannot be performed, which means that there is no information to be reconstructed at the decoding end. (3) The MR values of CASE_A to CASE_H can be up to 0.99, except CASE_G, because CASE_G is a preliminary allocation. , the discriminant is not added, so when the MR is greater than or equal to 0.5, the difficulty 3 occurs, that is, the total number of samples is greater than the resolution, so the compression sensing cannot be performed, and the picture cannot be displayed. 4) When CASE_A is equal to zero, since the band LL5 to the band HH2 are directly transmitted, the initial bpp will be higher and the quality will be better. (5) When the MR is higher, the bpp is higher. Because the discriminant NZR_band×M>band_s The ize will be established, so the frequency band will not be compressed and sensed, so the curve of CASE_A to CASE_F will become closer and closer to a certain value. Because baboon is a picture with more high-frequency signals, it is not common in general, so this picture will not be discussed first. The CASE_H curve of four pictures (randomly assigned), because MR=0.5 and 0.99, Bit_Rate Very large but the quality is up to 33db, so the H curve is not fully presented.

在時間複雜度方面也可以看到，在F曲線(使用非零個數比例分配次頻帶權重)的時候，編碼時間都會偏高，但是到了各頻帶分別不做壓縮感測直接傳送時，編碼時間有稍微下降一點點。 In terms of time complexity, it can also be seen that in the F-curve (using sub-band weights with a non-zero number ratio), the encoding time will be high, but when the frequency bands are directly transmitted without compression sensing, the encoding time There is a slight drop.

由第60圖至第63圖來看，除了baboon以外的三張圖片，都可以發現是A曲線(Lv2不經過壓縮感測直接傳送)在同一Bit_Rate所得到的品質會是最好的，也可以由表4.21觀察到當總非零個數接近時，例如lena和peppers，跑出來的圖片趨勢也會很接近。也可以觀察到MR越高時，編碼所花的時間也會稍微增加，因為取樣數變多，所以再編碼時會多花一點時間，但是增加時間不會很明顯，解碼部分則是MR越高的情況，速度稍微快一點點。這裡本發明也可以站在使用者的角度來看，如果使用者想要品質大約在30db~34db，本發明就會建議他使用A曲線(Lv2不做壓縮感測直接傳送)的方法，但是如果使用者想要的品質是28db~32db，本發明可能就會建議他使用B曲線(Lv3不做壓縮感測直接傳送)的方法，因為在品質差不多的情況下，Bit_Rate可以稍微降低一點，也是可以推薦給使用者考慮的。 From the 60th to 63th pictures, except for the three pictures except baboon, it can be found that the A curve (Lv2 is transmitted directly without compression sensing) will get the best quality in the same Bit_Rate. It is observed from Table 4.21 that when the total non-zero numbers are close, such as lena and peppers, the trend of the pictures that are ran out will be very close. It can also be observed that the higher the MR, the time spent on the encoding will increase slightly. Because the number of samples is increased, it takes a little more time to re-encode, but the increase time is not obvious, and the decoding part is the higher the MR. In the case, the speed is a little bit faster. Here, the present invention can also be viewed from the perspective of the user. If the user wants the quality to be about 30 db to 34 db, the present invention suggests that he use the A curve (Lv2 does not perform compression sensing for direct transmission), but if The quality that the user wants is 28db~32db. The present invention may suggest that he use the B curve (Lv3 does not perform direct transmission for compression sensing), because in the case of similar quality, Bit_Rate can be slightly lowered, and Recommended for users to consider.

六、針對baboon這張圖片探討HH1的必要性： 6. Exploring the necessity of HH1 for this picture of baboon:

根據上述實驗結果會發現，除了baboon這張圖片以外的HH1 都是用空矩陣所取代，那麼這節就來探討，如果也把baboon這張圖片的HH1也用空矩陣取代的話，效果會不會差很多。在上述實驗裡面，總共測試了四張圖片分別是lena、baboon、boat、peppers，其中有三張圖片(lena、boat、peppers)的HH1，因為在經過壓縮感測之後，矩陣內所有的值都未滿0.5，導致沒辦法進行重建的動作，所以在解碼端會以零矩陣取代，那如果把原本baboon的HH1也直接用零矩陣取代，在品質及複雜度會發生怎樣的改變，是本發明要觀察的重點。 According to the above experimental results, we will find HH1 in addition to this picture of baboon. They are all replaced by empty matrices, so this section will be discussed. If the HH1 of this picture of baboon is also replaced by an empty matrix, the effect will not be much worse. In the above experiment, a total of four pictures were tested as lena, baboon, boat, peppers, and there are three pictures (lena, boat, peppers) HH1, because after the compression sensing, all the values in the matrix are not If it is over 0.5, there is no way to rebuild it, so it will be replaced by a zero matrix at the decoding end. If the original HH1 of baboon is also directly replaced by a zero matrix, how the quality and complexity will change is the invention. The focus of observation.

在原本的架構中，直接把有關HH1的地方全部都刪除，包含壓縮感測、霍夫曼編碼、霍夫曼解碼、GPSR重建，然後解碼的地方設定一個零矩陣取代HH1。 In the original architecture, all the places related to HH1 are directly deleted, including compression sensing, Huffman coding, Huffman decoding, GPSR reconstruction, and then the decoding place sets a zero matrix instead of HH1.

這裡本發明只針對baboon進行測試，所以測試圖片只有baboon，大小為512^＊512，MR是使用固定參數，0.39、0.42、0.45，一樣會探討品質及時間複雜度。 Here, the present invention only tests for baboon, so the test picture is only baboon, the size is 512 ^* 512, MR uses fixed parameters, 0.39, 0.42, 0.45, and the quality and time complexity will be discussed.

由第64圖所示者可以發現，在同一個Bit_Rate下，其實品質是沒有差很多的，最多0.5是db，但是由第65圖可以看到，baboon的HH1在沒有經過壓縮感測，然後在解碼端用零矩陣取代時，編碼時間減少大約3%~5%，而解碼時間少大約25%~27%。由此可知，HH1的重要性真的很低，因此將在原架構中，把HH1的部分都移除，在解碼端由零矩陣取代。 From the figure shown in Figure 64, it can be found that under the same Bit_Rate, the quality is not much worse, up to 0.5 is db, but as can be seen from Figure 65, baboon's HH1 is not compressed and then When the decoder is replaced by a zero matrix, the encoding time is reduced by about 3% to 5%, and the decoding time is about 25% to 27% less. It can be seen that the importance of HH1 is really low, so in the original architecture, the HH1 part will be removed and replaced by a zero matrix at the decoding end.

七、與JPEG及JPEG2000比較： Seven, compared with JPEG and JPEG2000:

這節主要是把本發明的架構與JPEG及JPEG2000做比較， JPEG是目前很廣泛使用的圖像壓縮標準方法，他是基於離散餘弦變換，而JPEG2000是基於小波轉換的圖像壓縮標準，那本發明的架構也是有關壓縮方面的處理，因此想與現今的壓縮標準進行比較。 This section mainly compares the architecture of the present invention with JPEG and JPEG2000. JPEG is a widely used standard method of image compression. It is based on discrete cosine transform, and JPEG2000 is an image compression standard based on wavelet transform. The architecture of the present invention is also related to compression processing, so it is intended to be compressed with today. Standards are compared.

本發明首先找出JPEG及JPEG2000的編解碼程式，分別在文獻[11-12]，對於JPEG及JPEG2000本發明調整的參數為量化步階大小，然後會得到相對應的Bit_Rate及PSNR，測試圖片分別是lena、peppers、boat、baboon，大小皆為512^＊512，檔案格式為bmp檔。顯示圖片是四條，分別是proposed_Lv2、proposed_Lv3、JPEG、JPEG2000，會只選用proposed_Lv2及proposed_Lv3是因為上一小節跑出來的實驗結果，proposed_Lv2及proposed_Lv3效果最好，因此避免產生結果圖太過複雜，所以只選用兩條來加入JPEG及JPEG2000的評估裡。實驗一樣會以品質及時間複雜度分開評估。 The invention first finds the codec programs of JPEG and JPEG2000, respectively, in the literature [11-12], for the JPEG and JPEG2000, the parameters adjusted by the invention are the quantization step size, and then the corresponding Bit_Rate and PSNR are obtained, and the test pictures are respectively It is lena, peppers, boat, baboon, the size is 512 ^* 512, the file format is bmp file. The display picture is four, posing_Lv2, proposed_Lv3, JPEG, JPEG2000, only using proposed_Lv2 and proposed_Lv3 because the experimental results of the previous section, posing_Lv2 and proposed_Lv3 are the best, so avoiding the result is too complicated, so only Use two to add JPEG and JPEG2000 evaluations. Experiments will be evaluated separately in terms of quality and time complexity.

請參閱第66圖至第69圖所示者係JPEG、JPEG2000與本實驗室發展出架構proposed_Lv2及proposed_Lv3的RD曲線，表4.35到第70圖是複雜度的比較，其中旁邊的比例是以proposed_Lv2當做基準。那每張圖片因為JPEG及JPEG2000要調整QP值，所以執行出來的Bit_Rate比較難控制，因此四格表格都是分別找出相近的Bit_Rate來進行時間複雜度的比較。第69圖baboon在JPEG這條曲線可以看到Bit_Rate超過1.5bpp之後就沒有，是因為當QP調整到一定的值會發生重建回來圖型會有問題，所以只顯示到Bit_Rate小於1.5bpp。接下來以lena為代表，探討不同架構在不同Bit_Rate時，編解碼時間以及品質為何。 Please refer to Figures 66 to 69 for the JPEG and JPEG2000 and the RD curve developed by the laboratory with proposed_Lv2 and proposed_Lv3. Tables 4.35 to 70 show the complexity comparison. The ratio next to it is assumed_Lv2. Benchmark. That each picture because JPEG and JPEG2000 have to adjust the QP value, so the implementation of Bit_Rate is more difficult to control, so the four-grid table is to find a similar Bit_Rate to compare the time complexity. Figure 69: baboon in JPEG This curve can be seen after Bit_Rate exceeds 1.5bpp. It is because when QP is adjusted to a certain value, it will be rebuilt and the pattern will be problematic, so only the Bit_Rate is less than 1.5bpp. Next, with lena as the representative, explore different architectures. When using Bit_Rate, the codec time and quality.

第71圖是以lena為代表，來探討不同Bit_Rate時，編解碼時間以及品質的不同，可以發現proposed_Lv2、proposed_Lv3及JPEG這三個架構在Bit_Rate逐漸增大時，編碼時間沒有很明顯的增加，但是在JPEG2000卻是大幅度的增加。也可以特別注意到，proposed_Lv2在Bit_Rate等於1.3bpp時，品質來到38.89db，但是在JPEG2000只要Bit_Rate等於0.64bpp的時候，就可以到達38.25db這麼高的品質，但是編碼時間還是比本發明的還要慢。 Figure 71 is a representative of Lena, to explore the different Bit_Rate, codec time and quality differences, you can find the proposed_Lv2,proposed_Lv3 and JPEG three architectures in the Bit_Rate gradually increase, the coding time does not increase significantly, but In JPEG2000, it has increased dramatically. It can also be noted that the proposed_Lv2 quality comes to 38.89db when Bit_Rate is equal to 1.3bpp, but as long as Bit_Rate is equal to 0.64bpp in JPEG2000, it can reach the high quality of 38.25db, but the encoding time is still better than the present invention. Be slow.

由此可以發現JPEG2000在Bit_Rate越高的情況下，編碼時間會大幅度增加，因為本發明的架構也是使用小波轉換，所以本發明這邊就針對小波轉換在不同Bit_Rate，對JPEG2000編碼時間是否有直接影響做一個實驗。測試圖片一樣是選用四張，分別是lena、peppers、boat、baboon，解析度大小都為512^＊512，其結果如第72圖所示，可以發現JPEG2000在Bit_Rate比較低的時後，小波轉換時間占編碼時間的比率比較大，反過來當Bit_Rate比較高的時候，小波轉換時間占編碼時間的比率就比較低。這樣的結果也就說明了，在Bit_Rate較高的情況下小波轉換並沒有直接影響到JPEG2000，而是後續處理的Bit plane影響較大。 It can be found that the JPEG2000 has a higher encoding time in the case of higher Bit_Rate, because the architecture of the present invention also uses wavelet transform, so the present invention is directed to wavelet transform in different Bit_Rate, whether the JPEG2000 encoding time is directly Influence to do an experiment. The test picture is the same as four, which are lena, peppers, boat, baboon, and the resolution is 512 ^* 512. The result is shown in Figure 72. You can find the JPEG2000 after the Bit_Rate is low, the wavelet conversion time. The ratio of coding time is relatively large. Conversely, when Bit_Rate is relatively high, the ratio of wavelet conversion time to coding time is relatively low. This result also shows that the wavelet conversion does not directly affect JPEG2000 in the case of high Bit_Rate, but the Bit plane of subsequent processing has a greater impact.

因此可以觀察到，JPEG及JPEG2000在同一Bit_Rate下，大部分的品質都比本實驗室架構還高，但是以lena為例，在Bit_Rate大約在1.3bpp時，品值會比JPEG還高一些，在來看到時間複雜度，如果以第70圖的lena的圖片來看，可以發現在Bit_Rate接近的情況下，proposed_Lv2的編碼時間是0.67s，而JPEG2000的編碼時間是11.92s，本發明的架構比JPEG2000快11.25(1779%)秒，如果要發展DVC，分散式視訊編碼的觀點，也就是編碼簡單降低成本而解碼可以複雜，那本發明的架構就會很適用於此。 Therefore, it can be observed that JPEG and JPEG2000 are under the same Bit_Rate, most of the quality is higher than the lab architecture, but in the case of lena, when the Bit_Rate is about 1.3bpp, the value will be higher than JPEG. To see the time complexity, if you look at the picture of lena in Figure 70, you can find it in Bit_Rate. In the near case, the encoding time of proposed_Lv2 is 0.67s, and the encoding time of JPEG2000 is 11.92s. The architecture of the present invention is 11.25 (1779%) seconds faster than JPEG2000. If DVC is to be developed, the viewpoint of distributed video coding is The coding is simple to reduce the cost and the decoding can be complicated, and the architecture of the present invention is well suited for this.

步驟(e).針對各頻帶去進行壓縮感測處理後，再經round處理： Step (e). After performing compression sensing processing for each frequency band, it is processed by round:

其中本步驟的round處理係為：NZR_band×M=round(NZR_band×m×n×MR)；上述公式中，該NZR_band係指各頻帶的非零係數比，該M=m×n×MR為總取樣個數，該MR係為給定的量測值，最後經過round四捨五入變成整數。 The round processing of this step is: NZR_band×M=round (NZR_band×m×n×MR); in the above formula, the NZR_band refers to a non-zero coefficient ratio of each frequency band, and the M=m×n×MR is total The number of samples, the MR is a given measurement, and finally rounded to round to round to an integer.

步驟(f).分別送到霍夫曼編碼： Step (f). separately sent to Huffman coding:

該霍夫曼編碼法在許多標準中被採用，最著名的就是應用於失真影像壓縮標準的JPEG中。在JPEG標準中，影像被切割為8x8的區塊，每一區塊各自進行轉換編碼，轉換後的64個係數就是使用霍夫曼編碼法加以編碼、壓縮。由於霍夫曼編碼、解碼係為現有技術，在此不做贅述。 The Huffman coding method is used in many standards, most notably in JPEG for the distortion image compression standard. In the JPEG standard, images are cut into 8x8 blocks, each of which is converted and encoded. The converted 64 coefficients are encoded and compressed using Huffman coding. Since Huffman coding and decoding are prior art, no further description is made here.

另本發明解碼步驟(g)、(h)、(i)、(j)、(k)係相對應於前述的編碼方法原理，以進行解碼，因此步驟(g)、(h)、(i)、(j)、(k)在此不做贅述。 In addition, the decoding steps (g), (h), (i), (j), (k) of the present invention correspond to the foregoing coding method principle for decoding, so steps (g), (h), (i) ), (j), (k) are not described here.

本發明方法以發明專利申請案第100102685號的基礎架構下，並且提出以初步分配次頻帶權重來讓R-D效能變好。在來針對ENTROPY來估計Bit_Rate，本發明決定使用FLC及VLC來更實際貼近Bit_Rate的值，評估後發現VLC在同一Bit_Rate下，品質可以比ECL高大約6.26db(lena，1.2bpp)，再來針對信號的特性，像稀疏性(或稠密性)、Entropy值作為各頻帶MR分配的依據，從一開始次頻帶分成四個頻帶去做壓縮感測和初步分配，進而延伸至十六個次頻帶分開做壓縮感測及利用非零係數比當作次頻帶權重的分配比例，由實驗可以看出，在相同的Bit_Rate下，加入non-zero-ratio分配的架構，雖然計算量上有大幅提升，但是品質會比原始隨機分配架構高出10db左右。再來本發明評估若分配到的MR較高時，次頻帶所有係數做直接傳送的效果可能比經過CS還要好，實驗結果也發現Lv2也就是LL5、HL5、LH5、...、LH2，HH2都不經過壓縮感測，跟傳統壓縮感測隨機分配架構相比，在相同Bit_Rate下，品質會高出12db左右，但是可以根據使用者所要求不同的品質範圍，推薦不同的方法。最後評估HH1是否可以直接以零矩陣取代，實驗結果也發現HH1直接用零矩陣取代時，品質最多不會相差超過0.5db，也決定將HH1都用零矩陣取代。另外本發明也跟文獻[7]做比較，在相同的條件下，他們的lena結果是28.39db，而本發明的是32.10db，他們boat的結果是25.84db，本發明的是33.86db，明顯可以看到增加許多。最後也與現今的編碼方法JPEG及JPEG2000去做比較，雖然品質都會比較低，但是在編碼複雜度方面，本發明的架構比JPEG2000還要快1779%，而且本發明所使用的JPEG及JPEG2000都是MATLAB提供已經優化後的程式碼，而本發明的程式碼是尚未經過優化的處理，往後如果優化後就可以把本實驗室架構加入分散式視訊編碼來發展及研究。 The method of the present invention is based on the infrastructure of the invention patent application No. 100102685, and proposes to initially allocate the sub-band weights to make the R-D performance better. In order to estimate Bit_Rate for ENTROPY, the present invention decided to use FLC and VLC to be more realistic. It is close to the value of Bit_Rate. After evaluation, it is found that VLC is under the same Bit_Rate. The quality can be about 6.26db (lena, 1.2bpp) higher than ECL, and then the characteristics of the signal, such as sparsity (or denseness) and Entropy value. The basis of the band MR allocation is that the sub-band is divided into four bands from the beginning to perform compression sensing and preliminary allocation, and then extended to sixteen sub-bands for compression sensing and non-zero coefficient ratios for sub-band weight distribution. Proportion, it can be seen from the experiment that under the same Bit_Rate, adding the non-zero-ratio allocation architecture, although the calculation amount is greatly improved, the quality will be about 10db higher than the original random allocation architecture. Furthermore, the present invention evaluates that if the assigned MR is high, the effect of direct transmission of all coefficients of the sub-band may be better than that of CS. The experimental results also show that Lv2 is also LL5, HL5, LH5, ..., LH2, HH2. No compression sensing, compared with the traditional compression sensing random allocation architecture, under the same Bit_Rate, the quality will be about 12db higher, but different methods can be recommended according to different quality ranges required by users. Finally, it is evaluated whether HH1 can be directly replaced by a zero matrix. The experimental results also show that when HH1 is directly replaced by a zero matrix, the quality does not differ by more than 0.5 db at most, and it is decided to replace HH1 with a zero matrix. In addition, the present invention is also compared with the literature [7], under the same conditions, their lena result is 28.39db, and the present invention is 32.10db, the result of their boat is 25.84db, the invention is 33.86db, obviously Can be seen to increase a lot. Finally, compared with the current encoding methods JPEG and JPEG2000, although the quality will be relatively low, in terms of coding complexity, the architecture of the present invention is 1779% faster than JPEG2000, and the JPEG and JPEG2000 used in the present invention are both MATLAB provides the optimized code, and the code of the present invention is not yet optimized. After optimization, the laboratory architecture can be developed and researched by adding decentralized video coding.

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綜合以上說明，本發明係關於一種『小波壓縮感測影像的編碼方法』，且其未曾見於書刊或公開使用，誠符合發明專利申請要件，懇請鈞局明鑑，早日准予專利，至為感禱；需陳明者，以上所述乃是本發明之具體實施立即所運用之技術原理，若依本發明之構想所作之改變，其所產生之功能作用仍未超出說明書及圖式所涵蓋之精神時，均應在本發明之範圍內，合予陳明。 Based on the above description, the present invention relates to a "wavelet compression sensing image" "Code method", and it has not been seen in books or public use, it is in line with the requirements of the invention patent application, please ask the Bureau to express the patent, as soon as possible to grant the patent, to the pray; need to be clear, the above is the specific implementation of the present invention The technical principle of the application, if it is changed according to the concept of the present invention, the function of the invention is not beyond the spirit of the specification and the drawings, and should be combined with Chen Ming.

(a)、(b)、(c)、(d)、(e)、(f)、(g)、(h)、(i)、(j)、(h)‧‧‧方法步驟 (a), (b), (c), (d), (e), (f), (g), (h), (i), (j), (h) ‧ ‧ method steps

第1圖：係為本發明小波壓縮感測的編碼步驟流程圖。 Fig. 1 is a flow chart showing the encoding steps of the wavelet compression sensing of the present invention.

第2圖：係為本發明小波壓縮感測的解碼步驟流程圖。 Figure 2 is a flow chart showing the decoding steps of the wavelet compression sensing of the present invention.

第3圖：係為本發明小波壓縮感測所運用基Ψ進行稀疏性的表示圖。 Fig. 3 is a representation of the sparsity of the wavelet compression sensing used in the present invention.

第4圖：係為本發明小波壓縮感測所運用量測值表示矩陣圖。 Fig. 4 is a matrix diagram showing the measured values of the wavelet compression sensing used in the present invention.

第5圖：係為本發明小波壓縮感測線性量測過程圖。 Fig. 5 is a diagram showing the linear measurement process of wavelet compression sensing according to the present invention.

第6圖：係為本發明針對lena 4種CS量測方法的PSNR vs.Bit-rate的比較圖。 Fig. 6 is a comparison diagram of PSNR vs. Bit-rate for the four kinds of CS measurement methods of lena according to the present invention.

第7圖：係為本發明針對lena 4種CS量測方法的複雜度比較圖。 Fig. 7 is a comparison diagram of the complexity of the four kinds of CS measurement methods for lena according to the present invention.

第8圖：係為本發明針對lena不同小波階層的PSNR vs.Bit-rate的比較圖。 Figure 8 is a comparison of PSNR vs. Bit-rate for different wavelet levels of lena according to the present invention.

第9圖：係為本發明針對lena的不同階層的編解碼複雜度的比較圖。 Figure 9 is a comparison diagram of the codec complexity of different levels of lena for the present invention.

第10圖：係為本發明針對lena的DWT和DCT的非零係數、非零係數率、平均訊息量的比較圖。 Fig. 10 is a comparison diagram of non-zero coefficients, non-zero coefficient rates, and average message amounts of DWT and DCT for lena of the present invention.

第11圖：係為本發明針對lena的DWT和DCT的PSNR vs.Bit-rate比較圖。 Figure 11 is a comparison of PSNR vs. Bit-rate of DWT and DCT for lena of the present invention.

第12圖：係為本發明針對lena的DWT和DCT的編解碼複雜度比較圖。 Figure 12 is a comparison diagram of the codec complexity of DWT and DCT for lena of the present invention.

第13圖：係為本發明小波壓縮感測的四個子頻帶圖。 Figure 13 is a diagram showing four subbands of wavelet compression sensing of the present invention.

第14圖：係為本發明的lena的C_X_LH在經過門檻值5之前的訊號圖。 Figure 14 is a signal diagram of the C_X _LH of the lena of the present invention before passing the threshold value of 5.

第15圖：係為本發明的lena的C_X_LH在經過門檻值5之後的訊號圖。 Figure 15 is a signal diagram of the C_X _LH of the lena of the present invention after passing the threshold value of 5.

第16圖：係為本發明的lena的R_X_LH在經過門檻值5前的訊號圖。 Figure 16 is a signal diagram of the R_X _LH of the lena of the present invention before passing the threshold value of 5.

第17圖：係為本發明的lena的R_X_LH在經過門檻值5之後的訊號圖。 Figure 17 is a signal diagram of the R_X _LH of the lena of the present invention after passing the threshold value of 5.

第18圖：係為本發明的lena的統計C_X_LH和R_X_LH的特性圖。 Figure 18 is a characteristic diagram of the statistics C_X _LH and R_X _LH of the lena of the present invention.

第19圖：係為本發明的lena的C_X_LH和R_X_LH的R-D效能曲線圖。 Figure 19 is a graph showing the RD performance of C_X _LH and R_X _LH of the lena of the present invention.

第20圖：係為本發明的lena的C_X_LH和R_X_LH的R-D效能數據圖。 Figure 20 is a graph showing the RD performance data of C_X _LH and R_X _LH of the lena of the present invention.

第21圖：係為本發明的基本SQT來自SY JND模型顯示26.256像素/每度的分辨率圖。(其觀看距離係在60厘米) Figure 21: The basic SQT of the present invention is from the SY JND model showing a resolution map of 26.256 pixels per degree. (The viewing distance is 60 cm)

第22圖：係為本發明小波壓縮感測的四張測試圖片(a)lena(b)peppers(c)boat(d)baboon。 Figure 22: Four test pictures of wavelet compression sensing of the present invention (a) lena (b) peers (c) boat (d) baboon.

第23圖：係為本發明小波壓縮感測的測試平台設備。 Figure 23 is a test platform device for wavelet compression sensing of the present invention.

第24圖：係為本發明的lena 512^＊512 PSNR vs.Bit Rate的編解碼效能比較圖。 Figure 24 is a comparison diagram of the encoding and decoding performance of the lena 512 ^* 512 PSNR vs. Bit Rate of the present invention.

第25圖：係為本發明的peppers 512^＊512 PSNR vs.BitRate的編解碼效能比較圖。 Figure 25 is a comparison diagram of the codec performance of the peppers 512 ^* 512 PSNR vs. BitRate of the present invention.

第26圖：係為本發明的boat 512^＊512 PSNR vs.BitRate的編解碼效能比較圖。 Figure 26 is a comparison diagram of the codec performance of the boat 512 ^* 512 PSNR vs. BitRate of the present invention.

第27圖：係為本發明的baboon 512^＊512 PSNR vs.BitRate的編解碼效能比較圖。 Figure 27 is a comparison diagram of the codec performance of the baboon 512 ^* 512 PSNR vs. BitRate of the present invention.

第28圖：係為本發明的lena的FLC、VLC的計算複雜度比較圖。 Figure 28 is a comparison diagram of the computational complexity of the FLC and VLC of the lena of the present invention.

第29圖：係為本發明的peppers的FLC、VLC的計算複雜度比較圖。 Figure 29 is a comparison of the computational complexity of the FLC and VLC of the peppers of the present invention.

第30圖：係為本發明的boat的FLC、VLC的計算複雜度比較圖。 Fig. 30 is a comparison diagram of the calculation complexity of the FLC and VLC of the boat of the present invention.

第31圖：係為本發明的baboon的FLC、VLC的計算複雜度比較圖。 Figure 31 is a comparison diagram of the computational complexity of the FLC and VLC of the baboon of the present invention.

第32圖：係為本發明的lena的Entropy與huffman_avg的比較圖。 Figure 32 is a comparison of Entropy and huffman_avg of lena of the present invention.

第33圖：係為本發明的peppers的Entropy、huffman_avg的比較圖。 Figure 33 is a comparison of Entropy and huffman_avg of the pepperers of the present invention.

第34圖：係為本發明的boat的Entropy與huffman_avg的比較圖。 Figure 34 is a comparison of Entropy and huffman_avg of the boat of the present invention.

第35圖：係為本發明的baboon的Entropy、huffman_avg的比較圖。 Fig. 35 is a comparison diagram of Entropy and huffman_avg of the baboon of the present invention.

第36圖：係為本發明的量測向量合起來做VLC的示意圖。 Figure 36: is a schematic diagram of the VLC of the measurement vector of the present invention.

第37圖：係為本發明的量測向量分開做VLC的示意圖。 Fig. 37 is a schematic diagram showing the VLC of the measurement vector of the present invention.

第38圖：係為本發明分別將lena、peppers、boat及baboon的四個band一起做VLC處理及分開做處理的bits數比較圖。 Figure 38: This is a comparative comparison of the number of bits in which the four bands of lena, peppers, boat, and baboon are VLC processed and processed separately.

第39圖：係為本發明分別將lena及peppers的四個band一起做VLC處理及分開做處理的計算複雜度的比較圖。 Figure 39 is a comparison diagram of the computational complexity of the VLC processing and separate processing of the four bands of lena and pepper respectively.

第40圖：係為本發明分別將boat及baboon的四個band一起做VLC處理及分開做處理的計算複雜度的比較圖。 Figure 40 is a comparison diagram of the computational complexity of the four bands of boat and baboon for VLC processing and separate processing.

第41圖：係為本發明的lena圖和peppers圖512^＊512小波轉換五階各band的稀疏性與訊息量比較圖。 Fig. 41 is a comparison diagram of the sparsity and the amount of information of the fifth-order bands of the lena diagram and the Peppers diagram of the invention 512 ^* 512 wavelet transform.

第42圖：係為本發明的boat圖和baboon圖512^＊512小波轉換各band的稀疏性與訊息量。 Fig. 42 is a diagram showing the sparsity and the amount of information of each band of the 512 ^* 512 wavelet transform of the boat map and the baboon map of the present invention.

第43圖：係為本發明小波壓縮感測的lena圖和peppers圖各BAND的非零個數、稀疏度及非零係數比(NZR)的比較。 Figure 43 is a comparison of the non-zero number, sparsity and non-zero coefficient ratio (NZR) of each BAND of the wavelet compression sensing and the peppers diagram of the present invention.

第44圖：係為本發明的boat和baboon各BAND的非零個數、稀疏度及非零係數比(NZR)的比較。 Figure 44 is a comparison of the non-zero number, sparsity and non-zero coefficient ratio (NZR) of each BAND of the boat and baboon of the present invention.

第45圖：係為本發明所使用非零個數分配次頻帶權重的編碼流程圖。 Figure 45 is a flow chart showing the encoding of sub-band weights for non-zero numbers used in the present invention.

第46圖：係為本發明所使用非零個數分配次頻帶權重的解碼流程圖。 Figure 46 is a flow chart for decoding the sub-band weights assigned by the non-zero number used in the present invention.

第47圖：係為本發明的圖片影像重建失敗的態樣圖。 Fig. 47 is a view showing the failure of the image reconstruction of the present invention.

第48圖：係為本發明加入第一判別式的編碼、解碼的步驟流程圖。 Figure 48 is a flow chart showing the steps of encoding and decoding of the first discriminant according to the present invention.

第49圖：係為本發明加入第二、三判別式的編碼的步驟流程圖。 Figure 49 is a flow chart showing the steps of adding the second and third discriminant codes to the present invention.

第50圖：係為本發明加入第二、三判別式的解碼的步驟流程圖。 Figure 50 is a flow chart showing the steps of decoding the second and third discriminants of the present invention.

第51圖：係為本發明分別將lena及peppers的非零個數比例分配權重和全部隨機分配比較圖。 Fig. 51 is a comparison diagram of assigning weights and all random allocations of non-zero number ratios of lena and peers respectively.

第52圖：係為本發明分別將boat及baboon的非零個數比例分配權重和全部隨機分配比較圖。 Figure 52: This is a comparison map of the non-zero number distribution weights and all random allocations of boat and baboon.

第53圖：係為本發明分別將boat及baboon的非零個數比例分配權重和全部隨機分配的複雜度比較圖。 Fig. 53 is a comparison diagram of the complexity of allocating the non-zero number ratio of the boat and the baboon and the random allocation of the random allocation.

第54圖：係為本發明直接把其中幾個的band不經過壓縮感測直接做傳送的動作，且分成A、B、C、D、E五種CASE。 Fig. 54 is a view showing that the bands of the present invention directly transmit the bands directly without compression sensing, and are divided into five kinds of CASEs: A, B, C, D, and E.

第55圖：係為本發明的第54圖中的lena、peppers、boat、baboon圖片中各CASE所使用的MR值。 Fig. 55 is an MR value used by each CASE in the lena, peppers, boat, and baboon pictures in Fig. 54 of the present invention.

第56圖：係為本發明的lena 512^＊512的8種CASE的PSNR vs.bit_rate比較圖。 Fig. 56 is a comparison diagram of PSNR vs. bit_rate of 8 CASEs of the lena 512 ^* 512 of the present invention.

第57圖：係為本發明的peppers 512^＊512的8種CASE的PSNR vs.bit_rate比較圖。 Figure 57 is a comparison of PSNR vs. bit_rate for eight CASEs of the Peppers 512 ^* 512 of the present invention.

第58圖：係為本發明的boat 512^＊512的8種CASE的PSNR vs.bit_rate比較圖。 Fig. 58 is a comparison diagram of PSNR vs. bit_rate of eight CASEs of boat 512 ^* 512 of the present invention.

第59圖：係為本發明的baboon 512^＊512的8種CASE的PSNR vs.bit_rate比較圖。 Figure 59 is a comparison of PSNR vs. bit_rate of eight CASEs of the baboon 512 ^* 512 of the present invention.

第60圖：係為本發明的lena 512^＊512的8種CASE的編解碼時間圖。 Figure 60 is a codec timing diagram of eight CASEs of the lena 512 ^* 512 of the present invention.

第61圖：係為本發明的peppers 512^＊512的8種CASE的編解碼時間圖。 Figure 61 is a codec time chart of eight CASEs of the Peppers 512 ^* 512 of the present invention.

第62圖：係為本發明的boat 512^＊512的8種CASE的編解碼時間圖。 Fig. 62 is a codec time chart of eight CASEs of the boat 512 ^* 512 of the present invention.

第63圖：係為本發明的baboon 512^＊512的8種CASE的編解碼時間圖。 Fig. 63 is a codec time chart of eight CASEs of the baboon 512 ^* 512 of the present invention.

第64圖：係為本發明的baboon 512^＊512的HH1有經過壓縮感測及沒經過壓縮感測的PSNR vs.bit_rate比較圖。 Figure 64: The HH1 of the baboon 512 ^* 512 of the present invention has a PSNR vs. bit_rate comparison map that is subjected to compression sensing and is not subjected to compression sensing.

第65圖：係為本發明的baboon 512^＊512的HH1有經過壓縮感測及沒經過壓縮感測的PSNR vs.bit_rate的時間複雜度比較圖。 Fig. 65 is a time complexity comparison diagram of the PSNR vs. bit_rate of the baboon 512 ^* 512 of the present invention with compression sensing and no compression sensing.

第66圖：係為lena 512^＊512的JPEG、JPEG2000與本發明方法的PSNR vs.bit_rate比較圖。 Figure 66: Comparison of PSNR vs. bit_rate of JPEG, JPEG2000, and Lena 512 ^* 512, and the method of the present invention.

第67圖：係為peppers 512^＊512的JPEG、JPEG2000與本發明方法的PSNR vs.bit_rate比較圖。 Fig 67: is a system of JPEG peppers 512 ^* 512, PSNR vs.bit_rate comparing FIG JPEG2000 and methods of the present invention.

第68圖：係為boat 512^＊512的JPEG、JPEG2000與本發明方法的PSNR vs.bit_rate比較圖。 Figure 68: Comparison of PSNR vs. bit_rate for boat 512 ^* 512 JPEG, JPEG2000 and the method of the present invention.

第69圖：係為baboon 512^＊512的JPEG、JPEG2000與本發明方法的PSNR vs.bit_rate比較圖。 Figure 69: Comparison of PSNR vs. bit_rate for baboon 512 ^* 512 JPEG, JPEG2000 and the method of the present invention.

第70圖：係為lena 512^＊512、peppers 512^＊512、boat 512^＊512、baboon 512^＊512的JPEG、JPEG2000與本發明方法的PSNR vs.bit_rate比較圖。 Figure 70: Comparison of PSNR vs. bit_rate of lena 512 ^* 512, peppers 512 ^* 512, boat 512 ^* 512, baboon 512 ^* 512, and JPEG2000 of the method of the present invention.

第71圖：係為lena512^＊512的JPEG、JPEG2000在不同Bit_Rate的品質及編解碼時間測。 Figure 71: JPEG and JPEG2000 of lena512 ^* 512 in different Bit_Rate quality and codec time measurement.

第72圖：係為本發明的lena、peppers、boat、baboon的四張圖片在不同Bit_Rate的小波轉換所占JPEG2000編碼時間的百分比圖。 Figure 72: is a percentage of the JPEG2000 encoding time of the four images of the lena, peppers, boat, and baboon of the present invention in different Bit_Rate wavelet transforms.

第73圖：係為傳統的影像編碼架構圖。 Figure 73: It is a traditional image coding architecture diagram.

第74圖：係為CS影像編碼的基本架構圖。 Figure 74: The basic architecture of CS image coding.

第75圖：係為CS影像編碼的改良式架構圖。 Figure 75: An improved architecture diagram for CS image coding.

第76圖：係為發明申請案第100102685號的影像編碼架構圖。 Figure 76: Image coding architecture diagram of the invention application No. 100102685.

(a)、(b)、(c)、(d)、(e)、(f)‧‧‧方法步驟 (a), (b), (c), (d), (e), (f) ‧ ‧ method steps

Claims

一種小波壓縮感測影像編碼之方法係包含以下步驟：(a).輸入一張圖片，其解析度為m×n；(b).進行多階小波轉換；(c).各頻帶分別進行純量量化；(d).計算各頻帶的非零係數比並分配各次頻帶權重，其中該非零係數比係為各個頻帶的非零個數(non_zero_band)除以全部頻帶的非零個數總和(total_non_zero)；(e).針對各頻帶去進行壓縮感測處理後，再經round處理；(f).分別送到霍夫曼編碼。 A method for encoding wavelet compression sensing image includes the following steps: (a) inputting a picture with a resolution of m×n; (b) performing multi-order wavelet conversion; (c) performing purely for each frequency band Quantization; (d) calculating a non-zero coefficient ratio of each frequency band and assigning each sub-band weight, wherein the non-zero coefficient ratio is a non-zero number of each frequency band (non_zero_band) divided by a sum of non-zero numbers of all frequency bands ( Total_non_zero); (e). Perform compression sensing processing for each frequency band and then round processing; (f). Send Huffman encoding separately.

依據申請專利範圍第1項所述壓縮取樣影像編碼方法，另包含一解碼方法，其中該解碼方法係包含有以下步驟：(g).將接收到的霍夫曼編碼以進行霍夫曼解碼；(h).分別對各個頻帶進行梯度投影稀疏重建；(i).分別對各個頻帶進行反量化；(j).把各個頻帶合成一個矩陣進行反小波轉換；(k).重建影像並計算其峰值訊噪比值完成後，輸出該影像。 According to the compressed sampled image encoding method of claim 1, further comprising a decoding method, wherein the decoding method comprises the following steps: (g) receiving the Huffman encoding for Huffman decoding; (h) Gradient projection sparse reconstruction for each frequency band; (i) inversely quantizing each frequency band separately; (j) combining each frequency band into a matrix for inverse wavelet transform; (k) reconstructing the image and calculating its After the peak signal to noise ratio value is completed, the image is output.

依據申請專利範圍第1或2項所述小波壓縮感測影像編碼之方法，其中該round處理係為：NZR_band×M=round(NZR_band×m×n×MR)；上述公式中，該NZR_band係指各頻帶的非零係數比，該M=m×n×MR為總取樣個數，該MR係為給定的量測值，最後經過round四捨五入變成整數。 The method for encoding a wavelet compression sensing image according to claim 1 or 2, wherein the round processing is: NZR_band×M=round (NZR_band×m×n×MR); in the above formula, the NZR_band is The non-zero coefficient ratio of each frequency band, the M=m×n×MR is the total number of samples, the MR system is a given measurement value, and finally rounded to round to become an integer.

依據申請專利範圍第3項所述壓縮取樣影像編碼方法，其中該步驟(b)係進行五階小波轉換。 According to the compressed sample image coding method described in claim 3, wherein the step (b) is a fifth-order wavelet transform.

依據申請專利範圍第3項所述小波壓縮感測影像編碼之方法，其中該步驟(f)的霍夫曼編碼及該步驟(g)的霍夫曼解碼係皆以可變長度編碼方式(VLC)為之。 The method for encoding a wavelet compression sensing image according to claim 3, wherein the Huffman coding of the step (f) and the Huffman decoding of the step (g) are both variable length coding (VLC) ) for it.

依據申請專利範圍第3項所述小波壓縮感測影像編碼之方法，其中該步驟(k)的計算峰值訊噪比值的地方加入一第一判別式，該第一判別式係判別該峰值訊噪比值小於零時，將MR值進行累加，然後重新執行解碼；若該第一判別式係判別該峰值訊噪比值若大於零時，才輸出該影像。 According to the method for encoding the wavelet compression sensing image according to Item 3 of the patent application, wherein the step (k) calculates a peak signal-to-noise ratio value, and a first discriminant is added, and the first discriminant discriminates the peak signal noise. When the ratio is less than zero, the MR value is accumulated, and then the decoding is performed again; if the first discriminant determines that the peak signal to noise ratio value is greater than zero, the image is output.

依據申請專利範圍第3項所述小波壓縮感測影像編碼之方法，其中該步驟(e)中加入第二判別式，又該第二判別式係掃描HH1經過壓縮感測所得到的向量，若其全部值都未滿0.5，則設棄HH1，同時在解碼方法的步驟(i)中以相同大小的零矩陣來代替該HH1。 The method for encoding a wavelet compression sensing image according to claim 3, wherein the second discriminant is added to the step (e), and the second discriminant is a vector obtained by compressing the sensing of the HH1. If all of its values are less than 0.5, then HH1 is discarded, and at the same time, in the step (i) of the decoding method, the HH1 is replaced by a zero matrix of the same size.

依據申請專利範圍第3項所述小波壓縮感測影像編碼之方法，其中該步驟(e)前加入第三判別式，針對每個頻帶作步驟(e)的壓縮感測前的判別，若NZR_band×M大於該頻帶大小的話，就讓該頻帶直接傳送到步驟(f)霍夫曼編碼而不作壓縮感測，如果NZR_band×M小於該頻帶大小就續行下一個流程步驟。 The method for encoding a wavelet compression sensing image according to claim 3, wherein the third discriminant is added before the step (e), and the pre-compression sensing of the step (e) is performed for each frequency band, if the NZR _{If band} × M is larger than the size of the band, the band is directly transmitted to step (f) Huffman coding without compression sensing, and if NZR _band × M is smaller than the band size, the next process step is continued.