CN1822050A - Full phase anticosine double orthogonal transformation and its improving method for JPEG - Google Patents

Abstract

This invention relates to a total phase inverse cosine double orthogonal transformation method, which defines the transformation as [F]=[V][f][V< T >] and the inverse transformation as [f]=[V< -1 >][F][(V< T >)< -1 >] and uses the improved total phase inverse cosine double orthogonal transformation to replace 2-D scatter cosine transformation to simplify the quantification list so as to save computing time and increase quality of re-built images and coding compression ratio including the following steps: inputting an original image and a bit ratio to be divided into 8x8 pixel blocks and processed by total phase inverse cosine double orthogonal transformation to determine the quantification intervals based on the bit ratio to average the transformation coefficients, carrying out forecast coding to the DC coefficient and AC coefficient scan, variable-length coding, Harfmann entropy coding and outputting the bit sequence of a compressed image.

Description

Full phase place arc cosine biorthogonal conversion and improving one's methods thereof to JPEG

[technical field]: the invention belongs to the computer image processing technology field.

[background technology]: JPEG compression standard (ISO/IEC 10918-1|ITU-T Rec.T.81 Digitalcompression and coding of continuoustone still images) is widely used in still image coding, in JPEG, be called basic sequential process based on the process of the image compression encoding of discrete cosine transform (DCT).The cataloged procedure key step is: and 8 * 8 squareizations of image, two-dimension discrete cosine transform (Discrete CosineTransform, DCT), according to quantization table quantification, " it " (Zig-Zag) font scanning, Run-Length Coding, Huffman (Huffman) entropy coding.It is the inverse process of coding that receiving end decompresses, and through inverse quantization and anti-dct transform, obtains reconstructed image.The two-dimensional dct transform formula of 8 * 8 picture pieces [f] is [F]=[C] [f] [C ^T], wherein, [C] is 8 * 8 dct transform matrix, [C ^T] be the transposition of [C].Dct transform is orthogonal transformation, and the transposition of [C] is the contrary of [C], i.e. [C ^T]=[C ^-1].Therefore, by [f]=[C ^T] [F] [C] reconstructed image.The capable vector of [C] is to decompose base vector, [C ^T] column vector be synthetic base vector, dct transform is identical with decomposition base vector in the inverse transformation with synthetic base vector.

Dct transform is a kind of transform coding method commonly used in the JPEG Coding Compression Algorithm, has obtained in the digital image compression field using widely.Yet we find, orthogonal transformation is not optimum selection for image compression encoding, one of its shortcoming is the quantized interval different to different DCT coefficients by using, and the quantification when quantizing particularly to change compressibility needs complicated calculating, and quantization table also needs to account for certain memory headroom.

[summary of the invention]: the objective of the invention is to solve the prior art quantized interval different to different DCT coefficients by using, and quantization table complexity, the problem that need calculate in a large number provides a kind of full phase place arc cosine biorthogonal conversion and improving one's methods to JPEG thereof.

Full phase place arc cosine biorthogonal conversion method provided by the invention is that the full phase place arc cosine of two dimension biorthogonal conversion is defined as [F]=[V] [f] [V ^T], inverse transformation is defined as [f]=[V ^-1] [F] [(V ^T) ^-1], wherein [V] is full phase place arc cosine biorthogonal conversion matrix, general type is:

$V(m,n)=\left\{\begin{array}{ccc}1& m=0& 0\&le;n\&le;N-1\\ \frac{N-m+\sqrt{2}-1}{N}\cos \frac{m(2n+1)\mathrm{\&pi;}}{2N}& 1\&le;m\&le;N-1& 0\&le;n\&le;N-1\end{array}\right.,$ M, n represent the row and column of matrix V.

When N=8, full phase place arc cosine biorthogonal conversion matrix is:

$V=\left[\begin{array}{cccccccc}1.0000& 1.0000& 1.0000& 1.0000& 1.0000& 1.0000& 1.0000& 1.0000\\ 0.9088& 0.7704& 0.5152& 0.1808& -0.1808& -0.5152& -0.7704& -0.9088\\ 0.7408& 0.3072& -0.3072& -0.7408& -0.7408& -0.3072& 0.3072& 0.7408\\ 0.5624& -0.1320& -0.6640& -0.3760& 0.3760& 0.6640& 0.1320& -0.5624\\ 0.3904& -0.3904& -0.3904& 0.3904& 0.3904& -0.3904& -0.3904& 0.3904\\ 0.2368& -0.4184& 0.0832& 0.3552& -0.3552& -0.0832& 0.4184& -0.2368\\ 0.1152& -0.2792& 0.2792& -0.1152& -0.1152& 0.2792& -0.2792& 0.1152\\ 0.0344& -0.0984& 0.1472& -0.1736& 0.1736& -0.1472& 0.0984& -0.0344\end{array}\right].$

A kind ofly adopt above-mentioned full phase place arc cosine biorthogonal conversion method improving one's methods to JPEG, the present invention to the improvements of JPEG is, replace two-dimension discrete cosine transform with full phase place arc cosine biorthogonal conversion, adopt the quantized interval of homogeneous to quantize to all conversion coefficients, detailed process is as follows:

---input original image and bit rate;

---be divided into 8 * 8 block of pixels, carry out full phase place arc cosine biorthogonal conversion respectively;

---determine quantized interval according to bit rate, conversion coefficient is carried out homogeneous quantize;

---the predictive coding of DC coefficient and " it " font of ac coefficient scanning, Variable Length Code;

---the Huffman entropy coding;

---the bit sequence of output compressed image.

The receiving end decompression process is as follows:

---receive the compressed image bit sequence after conversion of input;

---the decoding of Huffman entropy;

---to DC coefficient and ac coefficient variable-length decoding;

---inverse quantization;

---anti-full phase place arc cosine biorthogonal conversion;

---obtain reconstructed image.

Advantage of the present invention and good effect: 1, the present invention is based on the theoretical and traditional arc cosine orthogonal transformation of all-phase digital filtering, to have proposed a kind of novel conversion be full phase place arc cosine biorthogonal conversion, and it is successfully applied to the compression of images field.2, the similarity of full phase place arc cosine biorthogonal conversion matrix [V] and DCT orthogonal transform matrix [C] be base vector row rate retinue sequence number increase and increase, difference is that each base vector of [C] is to wait mould, and the mould of the base vector of [V] increasing and decay with the row rate.This just makes full phase place arc cosine biorthogonal conversion coefficient have the character of high frequency attenuation.When the quantized interval that each conversion coefficient is adopted homogeneous quantizes, be equivalent to the effect that the dct transform low frequency coefficient carefully quantizes, high frequency coefficient slightly quantizes.Therefore can remove quantization table based on the complexity in the jpeg algorithm of dct transform.3, the great advantage compared with standard JPEG method of the improvement JPEG method that proposes of the present invention is, removed quantization table, because the quantization table of dct transform has 47 kinds of quantization steps, and adopts full phase place arc cosine biorthogonal conversion only to need a kind of quantization step, has saved the EMS memory occupation amount.Simplified calculating, improved encoding and decoding speed, shortened operation time greatly, adopted full phase place arc cosine biorthogonal conversion and homogeneous to quantize than the average fast 9.6713s operation time of adopting dct transform and corresponding quantification.Hardware is realized also fairly simple, and can reach and the essentially identical compression of images effect of dct transform.

[description of drawings]:

Fig. 1 compresses and the block scheme of rebuilding image with the inventive method;

Fig. 2 is the rate distortion curve of two kinds of scheme hypographs " lena ".

[embodiment]:

Embodiment 1

The present invention is defined as [F]=[V] [f] [V with the full phase place arc cosine of two dimension biorthogonal conversion ^T], inverse transformation is defined as [f]=[V ^-1] [F] [(V ^T) ^-1], wherein [V] is full phase place arc cosine biorthogonal conversion matrix.Different with orthogonal transform matrix, [V here ^-1] ≠ [V ^T], promptly decompose base vector (the row vector of [V]) and synthetic base vector ([V ^-1] column vector) be different, yet be biorthogonal between the two, constitute the reciprocal basis vector.The general type of the full phase place arc cosine biorthogonal conversion matrix [V] of the present invention's definition is:

$V(m,n)=\left\{\begin{array}{ccc}1& m=0& 0\&le;n\&le;N-1\\ \frac{N-m+\sqrt{2}-1}{N}\cos \frac{m(2n+1)\mathrm{\&pi;}}{2N}& 1\&le;m\&le;N-1& 0\&le;n\&le;N-1\end{array}\right.,$ M, n represent the row and column of matrix V.

When N=8

$V=\left[\begin{array}{cccccccc}1.0000& 1.0000& 1.0000& 1.0000& 1.0000& 1.0000& 1.0000& 1.0000\\ 0.9088& 0.7704& 0.5152& 0.1808& -0.1808& -0.5152& -0.7704& -0.9088\\ 0.7408& 0.3072& -0.3072& -0.7408& -0.7408& -0.3072& 0.3072& 0.7408\\ 0.5624& -0.1320& -0.6640& -0.3760& 0.3760& 0.6640& 0.1320& -0.5624\\ 0.3904& -0.3904& -0.3904& 0.3904& 0.3904& -0.3904& -0.3904& 0.3904\\ 0.2368& -0.4184& 0.0832& 0.3552& -0.3552& -0.0832& 0.4184& -0.2368\\ 0.1152& -0.2792& 0.2792& -0.1152& -0.1152& 0.2792& -0.2792& 0.1152\\ 0.0344& -0.0984& 0.1472& -0.1736& 0.1736& -0.1472& 0.0984& -0.0344\end{array}\right]$

Embodiment 2

The present invention has at first proposed a kind of novel conversion, promptly full phase place arc cosine biorthogonal conversion, and, be applied to compression of images with the dct transform in the full phase place arc cosine biorthogonal conversion replacement JPEG compression algorithm.The present invention adopts homogeneous to quantize to all conversion coefficients, and other parts of image compression encoding are identical with JPEG.The present invention is based on software realizes.

As shown in Figure 1, at first, import original image and desired bit rate, image is divided into 8 * 8 piece, piecemeal carries out full phase place arc cosine biorthogonal conversion, according to the selected quantized interval of the bit rate of setting, conversion coefficient is carried out homogeneous quantize, again the DC coefficient is carried out the difference predictive coding, the AC coefficient is carried out Zig-Zag scanning and Variable Length Code, Huffman code table according to standard carries out entropy coding then, and the code stream of output compressed image has been realized compression of images.At receiving end,, behind DC coefficient and AC coefficient variable-length decoding, the inverse quantization, carry out anti-full phase place arc cosine biorthogonal conversion again and can obtain reconstructed image through the decoding of Huffman entropy.

It should be noted that in the program flow diagram of Fig. 1, when carrying out the Huffman coding, for the DC coefficient, because be that the difference between the adjacent image piece is encoded, so before scanning after the quantification, want earlier the DC coefficient to be carried out pre-service.The original value that quantizes back DC is replaced to difference between the adjacent image piece.When the AC coefficient is encoded, consider that again 63 coefficients are that 16 companies, zero these two kinds of special circumstances or the like appear in zero-sum continuously entirely.

The technical scheme that under Matlab 6.5 environment the present invention is proposed has been carried out computer simulation experiment.Experiment obtains to draw a conclusion:

1. adopt full phase place arc cosine biorthogonal conversion, homogeneous quantized interval to be taken as compression of images rate and reconstructed image signal to noise ratio (S/N ratio) index at 58 o'clock, approximate with the index that adopts dct transform, quantize with the quantization table in the Joint Photographic Experts Group.

2. under other coding bit rates, technical scheme that the present invention proposes and standard JPEG scheme are also roughly the same aspect the subjective effect of reconstructed image and Y-PSNR.

As shown in Table 1 and Table 2:

The following two kinds of scheme performances of table 1 standard compression rate relatively

Test pattern	The DCT signal to noise ratio (S/N ratio)	The DCT ratio of compression	The DCT bit rate	APIDCBT signal to noise ratio (S/N ratio) (Q=58)	APIDCBT ratio of compression (Q=58)	APIDCBT bit rate (Q=58)
							Lena	35.8050	12.7988	0.6251	35.9495	12.9355	0.6185
boat	32.5423	9.0727	0.8818	32.6956	9.0276	0.8818
							zelda	37.7098	15.1793	0.5270	37.7133	15.4633	0.5174
modell	40.6479	19.0579	0.4198	40.6622	19.3199	0.4141
							milkdrop	38.0828	16.2525	0.4922	38.0591	16.8792	0.4740
girl3	39.6834	17.7325	0.4511	39.6243	18.2355	0.4387
							pyramid	37.4862	12.4048	0.6449	37.5888	12.3702	0.6467

Table 1 has provided 512 * 512 seven width of cloth images is adopted dct transform, quantizes and adopt full phase place arc cosine biorthogonal conversion (APIDCBT), homogeneous quantized interval to be taken as 58 experimental results of carrying out picture coding and reconstruction with the quantization table in the Joint Photographic Experts Group.

The following two kinds of scheme performances of the different compressibilitys of table 2 relatively

DCT quantization matrix Q doubly takes advantage of	DCT PSNR (db)	DCT bit rate (bpp)	The APIDCBT quantized interval	APIDCBT PSNR (db)	APIDCBT bit rate (bpp)
						Q*1	35.8050	0.6251	58	35.9495	0.6185
Q*2	33.6970	0.4037	116	33.6640	0.3967
						Q*3	32.3230	0.3177	174	32.2492	0.3117
Q*4	31.2489	0.2695	232	31.2605	0.2637
						Q*5	30.4005	0.2370	290	30.4732	0.2346
Q*6	29.6193	0.2161	348	29.8209	0.2140
						Q*7	28.9829	0.2001	406	29.2491	0.1986
Q*8	28.4465	0.1877	464	28.7618	0.1861
						Q*9	27.7804	0.1776	522	28.3483	0.1769

Table 2 has provided image " lena ", the experimental result of these two kinds of transform and quantization schemes under different coding bit rates and reconstructed image Y-PSNR.As can be seen from Table 1, the two compression effectiveness is basic identical.

The rate distortion curve of two kinds of transform and quantization scheme hypographs " lena " of being drawn by table 2 data as shown in Figure 2.As seen from Figure 2, when close coding bit rate, the improvement JPEG method that the present invention proposes slightly is better than standard JPEG method.

Claims (4)

1, a kind of full phase place arc cosine biorthogonal conversion method is characterized in that the present invention is defined as [F]=[V] [f] [V with the full phase place arc cosine of two dimension biorthogonal conversion ^T], inverse transformation is defined as [f]=[V ^-1] [F] [(V ^T) ^-1], wherein [V] is full phase place arc cosine biorthogonal conversion matrix, general type is:

$V(m,n)=\left\{\begin{array}{ccc}1& m=0& 0\&le;n\&le;N-1\\ \frac{N-m+\sqrt{2}-1}{N}\cos \frac{m(2n+1)\mathrm{\&pi;}}{2N}& 1\&le;m\&le;N-1& 0\&le;n\&le;N-1\end{array}\right.,$ M, n represent the row and column of matrix V.

2, full phase place arc cosine biorthogonal conversion method according to claim 1 is characterized in that when getting N=8, and full phase place arc cosine biorthogonal conversion matrix is:

$V=\left[\begin{array}{cccccccc}1.0000& 1.0000& 1.0000& 1.0000& 1.0000& 1.0000& 1.0000& 1.0000\\ 0.9088& 0.7704& 0.5152& 0.1808& -0.1808& -0.5152& -0.7704& -0.9088\\ 0.7408& 0.3072& -0.3072& -0.7408& -0.7408& -0.3072& 0.3072& 0.7408\\ 0.5624& -0.1320& -0.6640& -0.3760& 0.3760& 0.6640& 0.1320& -0.5624\\ 0.3904& -0.3904& -0.3904& 0.3904& 0.3904& -0.3904& -0.3904& 0.3904\\ 0.2368& -0.4148& 0.0832& 0.3552& -0.3552& -0.0832& 0.4148& -0.2368\\ 0.1152& -0.2792& 0.2792& -0.1152& -0.1152& 0.2792& -0.2792& 0.1152\\ 0.0344& -0.0984& 0.1472& -0.1736& 0.1736& -0.1472& 0.0984& -0.0344\end{array}\right].$

3, a kind ofly adopt the described full phase place arc cosine biorthogonal conversion method of claim 1 improving one's methods to JPEG, it is characterized in that the present invention to the improvements of JPEG is, replace two-dimension discrete cosine transform with full phase place arc cosine biorthogonal conversion, adopt the quantized interval of homogeneous to quantize to all conversion coefficients, detailed process is as follows:

---input original image and bit rate;

---be divided into 8 * 8 block of pixels, carry out full phase place arc cosine biorthogonal conversion respectively;

---determine quantized interval according to bit rate, conversion coefficient is carried out homogeneous quantize;

---the predictive coding of DC coefficient and " it " font of ac coefficient scanning, Variable Length Code;

---the Huffman entropy coding;

---the bit sequence of output compressed image.

4, according to claim 3 to the improving one's methods of JPEG, it is characterized in that the receiving end decompression process is as follows:

---receive the compressed image bit sequence after conversion of input;

---the decoding of Huffman entropy;

---to DC coefficient and ac coefficient variable-length decoding;

---inverse quantization;

---anti-full phase place arc cosine biorthogonal conversion;

---obtain reconstructed image.

Images