CN105894547A - Image processing method based on group-wave transformation compressed sensing - Google Patents

Abstract

The invention discloses an image processing method based on group-wave transformation compressed sensing. The method specifically comprises the steps that orthogonal group-wave transformation is carried out to an image at first, so that sparsity coefficients in each directional scale are obtained; then high-frequency coefficients of each scale are compressed, measured and encoded; and finally, orthogonal group-wave inverse transformation is carried out to stored low-frequency coefficients and recovered high-frequency coefficients, so that a recovered image is obtained. The method has the advantages that sparse representation of group-wave transformation is fully integrated into the compressed sensing; image geometrical characteristics are utilized to the hilt; redundancy and resource waste caused by traditional Nyquist sampling theories are eliminated; texture information such as directions and scales of images can be further excavated; and high-definition images can be recovered when only a few of sampling points can be provided. In comparison with the existing method of wavelet transformation compressed sensing, the method disclosed by the invention has obvious advantages and has very broad application prospect in image processing.

Description

Image processing method based on group wave conversion compressed sensing

Technical field

The method that the present invention relates to image procossing, is at a kind of image based on group ripple (Grouplet) conversion compressed sensing Reason method.

Background technology

Compressive sensing theory^[1-3]Mainly for sparse signal or compressible signal, while obtaining signal, data are entered The compression that row is suitable, its sample frequency is far below nyquist frequency, can reduce sampled data simultaneously, eliminates bulk redundancy, joint Save memory space, but contain the enough quantity of information that can reconstruct primary signal.Meanwhile, compressed sensing is by traditional data Gather and unite two into one with data compression, but need not the data encoding algorithm of complexity, suitable reconstruction can be used when necessary to calculate Method recovers abundant data point from the data that compressed sensing obtains.Compressive sensing theory is to utilize signal and image just That hands under base openness is carried out as priori basis, and the orthogonal basis generally selected is the orthogonal basis of wavelet transformation, great Liang Yan Study carefully and have turned out compression sensing method based on wavelet transformation^[4-8]Accurate original image can be reconstructed.But due to small echo Conversion limitation on geometric direction, it is impossible to the geometric scale that adapting to image is complicated well, causes the image of recovery not Original image can be approached well.Based on this, further provide Grouplet conversion^[19]This brand-new alternative approach carrys out generation The first step rarefaction carried out as compressed sensing for wavelet transformation.Grouplet conversion is to convert Multi-Scale Haar Lifting obtains further, and it can change the structure of base adaptively according to the geometry regularity of image, it is achieved to signal Rarefaction representation, it is thus achieved that sparse signal more more preferable than wavelet transformation to provide more preferable basic condition for the reconstruct of compressed sensing.Base The existing substantial amounts of literature research of compression of images perception in wavelet transformation, as document [4] is premised on compression of images, for little Wave conversion compressive sensing theory proposes new method for compressing image, and wavelet transformed domain is extended to Wavelet-Packet Domain, significantly Improve reconstruction accuracy.Furthermore, the method for document [7] the wavelet transformation compressed sensing that has been then system introduction, and for image sampling The dialectical relationship of rate and reconstruction quality etc. has carried out description of test.Additionally, document [19] is proposed in 2008 by Mallat A kind of new multi-scale transform method, in full detailed interior of each side such as the principle of system introduction Grouplet conversion, algorithm Hold, be the classic of the method.The domestic research for Grouplet conversion is the most limited, and the existing article of major part is also right The discussion of its principle, for its apply the most limited.

Summary of the invention

Based on above-mentioned background technology, the present invention proposes a kind of compression of images cognitive method based on group wave conversion, respectively It is analyzed with existing compression sensing method based on wavelet transformation, according to error requirements and accuracy specifications, obtains Image can to greatest extent close to even completely in original image, can obtain the complex texture of image to greatest extent, meanwhile, Use brand-new compressive sampling method, both reduced big view data, save internal memory, save again for the high hardware required for transmission Requirement.

The present invention takes techniques below scheme to realize above-mentioned purpose.Compression of images perception process side based on group wave conversion Method, is blended in group wave conversion rarefaction representation in compressed sensing, and detailed process is: first, and image is carried out orthogonal systems wave conversion Obtain the sparse coefficient on all directions yardstick, retain low frequency coefficient constant；Then, only it is compressed each yardstick high frequency coefficient surveying Amount coding, after requiring to store and transmit for difference, uses compressed sensing restructing algorithm to recover high frequency coefficient； Finally, the high frequency coefficient of the low frequency coefficient of preservation Yu recovery is carried out orthogonal systems ripple inverse transformation, thus the image being restored；

Said process is represented by following formula: y=Φ x=Φ Ψ f；

Wherein: Ψ is group wave conversion base, and Φ represents calculation matrix, and primary signal x is divided under the effect of group wave conversion base Ψ Solve the signal f being there is K degree of rarefication；Measured value y is obtained after measuring coding.

Based on group wave conversion compressed sensing image processing algorithm particularly as follows:

(1) image is carried out orthogonal systems wave conversion, obtain the radio-frequency component on all directions yardstick and low-frequency component Band coefficient.

(2) carry out rarefaction for the radio-frequency component (the most sparse part) obtained, obtain the sparse coefficient table in all directions Show；Low-frequency component then keeps constant.

(3) set up random measurement matrix, respectively the sparse matrix of different directions is measured, obtain measurement coefficient value； Low frequency coefficient keeps constant.

(4) utilize compressed sensing classic algorithm, such as OMP algorithm and iterative algorithm, respectively the high frequency coefficient after measuring is entered Line reconstruction, obtains the reconstruct component in all directions.

Each component is carried out orthogonal systems ripple inverse transformation, obtains reconstructing image.

The beneficial effects are mainly as follows following aspect:

(1) group wave conversion method overcomes wavelet transformation and can only catch limited directional information on image procossing, to multiple The defect that miscellaneous texture and marginal information can not effectively be extracted；

(2) method proposed has merged multi-scale transform and the compressive sensing theory of advanced person, can utilize to greatest extent The geometric properties of image, eliminates redundancy and the waste of resource that conventional Nyquist sampling theory causes, can enter one simultaneously Step excavates the texture information of the direction of image, yardstick etc. so that even if little sampling number also can recover more visible figure Picture element amount；

(3) compare with existing method, the method clear superiority in terms of image procossing, can apply to image simultaneously The various aspects such as denoising, compression of images, image co-registration, embody the advantage of the method from objective evaluation.May be used to image procossing Every field.Compared with additive method, this image processing method has clear superiority, has wide application prospect, especially It is in military field.

Accompanying drawing explanation

Fig. 1 is compressed sensing procedure chart；

Fig. 2 is the composition schematic diagram that group wave conversion decomposes；

Fig. 3 is compressed sensing process detailed maps；

Fig. 4 is compressed sensing process schematic based on group wave conversion；

Fig. 5 a is that in group wave conversion compressed sensing, compression ratio is reconstruct image when 0.1；

Fig. 5 b is that in group wave conversion compressed sensing, compression ratio is reconstruct image when 0.2；

Fig. 5 c is that in group wave conversion compressed sensing, compression ratio is reconstruct image when 0.3；

Fig. 5 d is that in group wave conversion compressed sensing, compression ratio is reconstruct image when 0.4；

Fig. 5 e is that in group wave conversion compressed sensing, compression ratio is reconstruct image when 0.5；

Fig. 5 f is that in group wave conversion compressed sensing, compression ratio is reconstruct image when 0.6；

Fig. 5 g is that in group wave conversion compressed sensing, compression ratio is reconstruct image when 0.7；

Fig. 5 h is that in group wave conversion compressed sensing, compression ratio is reconstruct image when 0.8；

Fig. 5 i is that in group wave conversion compressed sensing, compression ratio is reconstruct image when 0.9；

Fig. 6 is the PSNR curve chart reconstructing image under group wave conversion compressed sensing difference compression ratio；

Fig. 7 a is that in wavelet transformation compressed sensing, compression ratio is reconstruct image when 0.1；

Fig. 7 b is that in wavelet transformation compressed sensing, compression ratio is reconstruct image when 0.2；

Fig. 7 c is that in wavelet transformation compressed sensing, compression ratio is reconstruct image when 0.3；

Fig. 7 d is that in wavelet transformation compressed sensing, compression ratio is reconstruct image when 0.4；

Fig. 7 e is that in wavelet transformation compressed sensing, compression ratio is reconstruct image when 0.5；

Fig. 7 f is that in wavelet transformation compressed sensing, compression ratio is reconstruct image when 0.6；

Fig. 7 g is that in wavelet transformation compressed sensing, compression ratio is reconstruct image when 0.7；

Fig. 7 h is that in wavelet transformation compressed sensing, compression ratio is reconstruct image when 0.8；

Fig. 7 i is that in wavelet transformation compressed sensing, compression ratio is reconstruct image when 0.9；

Fig. 8 is the PSNR curve comparison reconstructing image under group ripple compressed sensing compression ratio different from wavelet transformation compressed sensing Figure；

In figure: (1) is the PSNR curve of group ripple compressed sensing, and (2) are the PSNR curves of wavelet transformation compressed sensing；

Fig. 9 is the SAR original image for being reconstructed；

Figure 10 a is the SAR image through organizing wave pressure contracting sensing reconstructing, PSNR=24.52；

Figure 10 b is the SAR image through the reconstruct of wavelet transformation compressed sensing, PSNR=18.31.

Detailed description of the invention

Below in conjunction with accompanying drawing, implement principle, simulation example etc. and the present invention made illustrate further, see accompanying drawing and say Bright.

1. the ultimate principle of compression of images perception based on group wave conversion and algorithm:

The principle of 1.1 groups of wave conversions:

As in figure 2 it is shown, group wave conversion decomposes the calculating including associated domain layer and coefficient layer, wherein coefficient layer includes low frequency system The levels of detail that the average layer of number composition and high frequency coefficient are constituted.In group wave conversion, the performance to conversion of finding of associated domain has very Big impact.Group wave conversion uses block matching algorithm to find associated domain, and this method can accurately reflect each pixel Change, but can not be the most adaptive according to picture structure selected directions.Coefficient layer comprises again average layer and levels of detail two Individual sublayer, the process to signal is i.e. that the calculating to mean coefficient and detail coefficients processes.The object of Grouplet conversion is permissible It is image itself, it is also possible to be image coefficient after other converts.Group wave conversion uses a kind of similar Haar wavelet transformation Fast transform approach.Orthogonal systems wave conversion calculates associated domain based on Embedded sampling grid, thus can not self adaptation The baroque image of representing grain；Tight frame group wave conversion then introduces the computational methods in cause and effect multi-scale coupling territory and changes Enter this problem, and achieve good effect, but still can not preferably meet stricture of vagina at the regional area that some texture structures are complicated The structure of reason.

1.2 compressed sensing principles:

Compressive sensing theory is a kind of imaging theory proposed on the basis of rarefaction representation and optimum theory, pass therein Key is to compress and sample to carry out simultaneously.Compressed sensing mainly includes that the rarefaction representation of signal, calculation matrix are measured and calculate reconstruct 3 Individual aspect.

If the primary signal x ∈ R of a length of N^N×1, one-dimensional signal can be expanded into for 2D signal, y is the sight of length M Survey signal, then use orthogonal basis or the rarefaction representation of redundant dictionarySparse coefficient y can be expressed as:

Wherein,I is unit matrix.Regulation sparse coefficient y only has k nonzero coefficient, Namely in addition to a few coefficients value is relatively big, other major part coefficients are the least or close to 0, nowIt is the dilute of signal x Dredge base or rarefaction representation.

Next need sparse coefficient to be projected on calculation matrix ψ, obtain M the measured value of y, i.e.

Wherein, ψ ∈ R^M×N, and M ＜ ＜ N, i.e. the number of equation is fewer than the number of unknown number.Find out that this is one and owes fixed Problem, without determining solution.But under meeting k ＜ ＜ M premise, can obtain determining solution.Equidistant character is retrained furthermore, it is necessary to meet.

In summary, compressed sensing equation is y=Φ x=Φ Ψ s=Θ s.Wherein, by original calculation matrix Φ conversion For Θ=Φ Ψ, being defined as perception matrix, solve s approaches valueThen the reconstruction value of original signal isPerception matrix Embodying compressed sensing is the process that a compression is carried out with sampling simultaneously, is the marrow of compressive sensing theory, its detailed process See Fig. 3.

1.3 compressed sensing principle based on group wave conversion and algorithms:

Compressive sensing theory is a kind of imaging theory proposed on the basis of rarefaction representation and optimum theory, pass therein Key is to compress and sample to carry out simultaneously, and its detailed process decomposed is shown in Fig. 1.

Whole compressed sensing process is represented by following formula: y=Φ x=Φ Ψ f.Wherein primary signal x is at sparse transformation base The signal f with K degree of rarefication it is decomposed under the effect of Ψ.Φ represents calculation matrix, obtains measured value y after measuring coding.Change Simple: y=Af.A=Φ Ψ is referred to as perception matrix, the feature that integrating representation compression and sampling are carried out simultaneously.Above theoretical Under, it is that the rarefaction representation of signal, encoding measurement and three steps of restructing algorithm are discussed in detail by compressed sensing procedure decomposition.

The premise of compressed sensing be signal must be can be sparse, and major part image be incompressible in time domain, i.e. The most sparse so that convert the signal into can be sparse frequency domain on.Image has not only resolved into low frequency after wavelet transformation And high frequency, but also comprise the information in multiple directions, there is its unrivaled advantage, but owing to it has a singularity, Do not have the unusual even face of good line unusual, it is impossible to accurately to approach the grain details of image.Grouplet converts^[18]It is to pass through Haar transform is lifted out a stable several picture so that its base can be along with image geometry under different scale Change and change, thus the geometric properties of image can be utilized to greatest extent.Meanwhile, group ripple proposes the concept of associated domain, It is to organize ripple base to approach the geometry flow of the arbitrary shape in zonule, and the geometry that in image, relatedness is the longest can be approached Structure, fully compensate for the deficiency of wavelet transformation.So, use orthogonal systems wave conversion to extract sparse signal as compressed sensing Means, do for restructing algorithm and prepare more accurately.

First, orthogonal systems wave conversion is introduced.Multi-Scale Haar conversion is obtained by group wave conversion by weighted average.Flat All signals are initialized as input signal: a [n]=f [n], n ∈ G₀, from primary signal f [n], calculate average signal a's [n] The support size of average core, and be saved in newly-built array s [n].In initialization procedure, due to a [n]=f [n], the most averagely Core obtains a signal coefficient, so s [n]=1.

For from 1 to 2^JYardstick 2^jIn,In institute a littleAccording to a kind of predefined sequential packet.OrderIn Sampled point number be N_j, make α_jFor at 1≤n≤N_jWithBetween reversibility map.For from 1 to N_jN, Mei GedianAll associate a pointGroup wave conversion calculates two association averages Between standardization detail coefficients and new weighted mean:

$d_j\[\tilde{m}\]=(a\[\tilde{m}\]-a\[m\])\frac{\sqrt{s\[m\]s\[\tilde{m}\]}}{\sqrt{s\[m\]+s\[\tilde{m}\]}}$

$\hat{a}=\frac{s\[m\]a\[m\]+s\[\tilde{m}\]a\[\tilde{m}\]}{s\[m\]+s\[\tilde{m}\]}$

And new weighted meanBe weighted value s [m] by two average points andAnd update:

$\hat{s}=s\[m\]+s\[\tilde{m}\].$

These values are saved inPosition on.

Especially, in out to out 2^j=2^JOn, mean coefficient is normalized:

$\∀m\∈G_J,a_J\[m\]=a\[m\]\sqrt{s\[m\]}.$

So, group wave conversion is just by signal f [n] that size is N and Grouplet coefficient raceAssociate. The expression of group ripple refers not only to the expression of these coefficients, also includes N (1-2^-J) individual multi-scale coupling domain coefficient

Arrive this, image is carried out complete orthogonal systems wave conversion, has reached sparse purpose, obtain a series of sparse system Number.

After completing the group wave conversion rarefaction representation of compressed sensing, next need rarefaction representation result is measured volume Code.The top priority measuring sparse matrix is structure calculation matrix Φ.Calculation matrix must is fulfilled for retraining isometry condition (RIP), i.e. selected calculation matrix Φ and group wave conversion base Ψ is uncorrelated.Common calculation matrix is gaussian random matrix, it Can be M*N and each value meets the distribution of Ν (0,1/N) independent normal and obtains by selecting size.Gauss measurement square The advantage of battle array is that it is almost the most uncorrelated with any sparse signal, thus required pendulous frequency is minimum.Utilize gaussian random Sparse matrix after group wave conversion is measured by calculation matrix, it is thus achieved that calculation matrix y.

Can obtain from above two steps, calculation matrix Φ together constitutes compressed sensing process with group wave conversion base Ψ Perception matrix A, has been used for compressed sensing sampling and has compressed simultaneously carrying out of task.

It follows that need the calculation matrix y to obtaining to be reconstructed, it is desirable to Perfect Reconstruction as far as possible goes out original data, Or under meeting certain error condition, complete reconstruct.Compression sampling result utilize orthogonal matching pursuit algorithm (OMP) carry out Reconstruct.The basic thought of OMP algorithm is in iterative process each time, selects from over-complete dictionary of atoms (i.e. perception matrix A) Select the atom mated most with signal to build sparse bayesian learning, and obtain signal and represent surplus, then proceed to select and signal margin The atom mated the most, after the iteration of certain number of times, signal just by some atom linear expression, and can pass through recurrence The atom set selected is orthogonalized to ensure the optimality of iteration, thus reduces iterations.Experiment shows, to solid After determining N-dimensional discrete signal Gaussian matrix measurement sparse for K-, as long as complexity M=Ο (KlgN), OMP algorithm just can be with pole Big probability accurate reconstruction goes out signal.The concrete iterative process of OMP algorithm is:

(1) initialize: surplus r₀=Y, iterations n=1, index value setHere,Represent Empty set；

(2) correlation coefficient μ is calculated, whereinAnd by corresponding for maximum in μ Index value is stored in J；

(3) support collection Φ is updated_Λ, wherein Λ=Λ ∪ J₀；

(4) utilizeCalculate

(5) utilizeSurplus is updated；

(6) if | | r_new-r||≥ε₂, then r=r is made_new, n=n+1, jump procedure (2) circulation performs, and otherwise, stops repeatedly Generation.

Finally, utilize orthogonal systems ripple inverse transformation that the data of reconstruct are reverted to pictorial form.Determining of orthogonal systems ripple inverse transformation Justice is to reconstruct original input signal f [n], i.e. from group wave system number

$f\[n\]=\underset{j=1}{\overset{J}{\mathrm{\Σ}}}\underset{\tilde{m}\∈G_j}{\mathrm{\Σ}}{d}_j\[\tilde{m}\]g_{j,\tilde{m}}\[n\]+\underset{m\∈G_J}{\mathrm{\Σ}}{a}_J\[m\]h_{J,m}\[n\]$

Being similar to quick Haar inverse transformation, quickly group ripple inverse transformation is to overturn each group in the reverse direction of positive-going transition (group) operation, simultaneously yardstick 2^jFrom out to out 2^JIt is minimized yardstick 1.

In out to out 2^JOn, the size of average array needs to recalculate estimation according to associated domain.Initialization step s [m]=1.

ForHave

And work asShi YouAt yardstick 2^JOn, the normalized process of mean coefficient is reversed to:

$\∀m\∈G_J,a_J\[m\]=\frac{a_J\[m\]}{\sqrt{s\[m\]}}.$

Each group conversion (Grouping) can be inverted on each yardstick, definition:

Wherein j is from J to 1, and n is from N_JTo 1.In order to invert group's conversion, the weighted value of mean coefficient is by reversionUpdate:

$\hat{s}=s\[m\]-s\[\tilde{m}\].$

Meanwhile, more preferable yardstick mean coefficient by the defined conversion of inversion formula from the mean coefficient of more large scale and Detail coefficients is calculated:

$a\[\tilde{m}\]=a\[m\]+d_j\[\tilde{m}\]\frac{\sqrt{\hat{s}}}{\sqrt{s\[\tilde{m}\]s\[m\]}},$

$\tilde{a}=a\[m\]-d_j\[\tilde{m}\]\frac{\sqrt{s\[\tilde{m}\]}}{\sqrt{\tilde{s}s\[m\]}}.$

The value obtained after these reconstruct is updated toIn.On all of yardstick and all of group It is circulated the input signal that the inverse final result calculated can obtain reconstructing, it may be assumed that

A [m]=f [m], m ∈ G₀。

Complete the conversion process of whole compressed sensing to this, pass through the Y-PSNR (PSNR) image to recovering simultaneously Being evaluated, the definition of PSNR is:

$PSNR=10\×\lg \left(\frac{N^2}{{\left|x-y\right|}^2}\right)$

Wherein, x and y is original image and the data recovering image respectively.Experience, PSNR is the biggest, the reconstruct of image Effect is the best.

In sum, the schematic diagram of compressed sensing based on group wave conversion, as shown in Figure 4, it concretely comprises the following steps:

Step 1: original image 1 utilizes the direct transform 2 of orthogonal systems ripple carry out sparse transformation 3, obtains the height in all directions Frequently composition 5 and a low frequency coefficient 4.

Step 2: carry out rarefaction for the radio-frequency component 5 (the most sparse part) obtained, obtain the sparse system in all directions Number represents；Low-frequency component then keeps constant.

Step 3: set up Gauss measurement matrix, respectively the sparse matrix of different directions is measured, obtain measurement coefficient Value；Storing 7 by transmission or to store or transmit, low frequency coefficient 9 keeps constant.

Step 4: utilize OMP algorithm and iterative algorithm, respectively the high frequency coefficient 8 after measuring is compressed sensing reconstructing 10, obtain the reconstruct component in all directions.

Step 5: utilize the inverse transformation 12 of orthogonal systems ripple that each component carries out sparse inverse transformation 11, obtains reconstructing image 13, Calculate PSNR simultaneously and image is carried out quality evaluation.

2. simulation study:

According to above-mentioned step, emulated by Matlab and study Lena imagery exploitation group under the conditions of different sample rate Lena imagery exploitation wavelet transformation under the conditions of the difference that the compression sensing method of wave conversion is reconstructed, and different sample rate The difference that compression sensing method is reconstructed, the excellence of two kinds of methods of relative analysis.

Here select is the Lena image of standard, and size is 256 × 256.Define at this, if the size of calculation matrix is M × N, wherein M ＜ ＜ N, it is stipulated that compression ratio is M/N.Compression ratio is the least, and sample rate is the lowest, therefore can characterize with compression ratio Sample rate.

First, the Lena of the compression sensing method reconstruct of utilization group wave conversion under the conditions of the different compression ratios of comparison (sample rate) Image, as it is shown in figure 5, represent compression ratio reconstruction image from 0.1 to 0.9 time.Corresponding, Fig. 6 is that compression ratio is from 0.1 to 0.9 Time reconstruct image PSNR curve.

From the visual effect of reconstruct image it can be seen that under all compression ratios, equal restructural goes out original image.By Fig. 5 a, Even if 5b is it can be seen that use the lowest compression ratio also can reconstruct basic image outline, simply have fuzzy at image detail, Edge does not highlights, and curve is the most smooth.Reconstruct image is along with the increase of compression ratio, and definition has had the lifting of matter step by step. The most substantially whole image is reconstructed to Fig. 5 d.By Fig. 5 f it can be seen that the compressed sensing of utilization group wave conversion at compression ratio is Complete image can be gone out by Perfect Reconstruction when 0.6, approach perfection.On the other hand, it can be seen that along with the increasing of compression ratio from PSNR Greatly, PSNR incrementally increases, and the PSNR value change between adjacent compression ratio is slowly increased, it was demonstrated that reconstruction coefficients is also constantly being approached Entirely.

Afterwards, the Lena utilizing the compression sensing method of wavelet transformation to reconstruct under the conditions of comparing different compression ratios (sample rate) Image, as it is shown in fig. 7, represent compression ratio reconstruction image from 0.1 to 0.9 time equally.From Fig. 7 a, 7b, 7c it can be seen that based on The compression sensing method of wavelet transformation can not reconstruct image when compression ratio is relatively low, along with the increase of compression ratio, reconstruct image Quality displays the most gradually.And reconstruct image and the most substantially recovered when compression ratio reaches 0.6.This indicates that, at base In the compressed sensing of wavelet transformation, sample rate can not be too low, in order to avoid reconstruct image fault is serious.

By the emulation of two steps above, contrast in terms of image reconstruction quality and evaluation criterion PSNR two Analyze.The PSNR curve of compressed sensing reconstruct image based on group wave conversion reconstructs image with compressed sensing based on wavelet transformation PSNR curve comparison as shown in Figure 8.

Comparison diagram 5 and Fig. 7, compression sensing method based on group wave conversion is substantially better than compressed sensing based on wavelet transformation Method, especially group wave conversion compression sensing method just can reconstruct the result approaching original image under extremely low compression ratio Image, distortion rate is relatively low, and picture quality does not the most affect visual discrimination.Fig. 8 correspondingly has also confirmed this conclusion, base PSNR value entirety in the compression sensing method of group wave conversion is all higher than the PSNR value of compression sensing method based on wavelet transformation, It is especially apparent when sample rate is relatively low.Simulation results proves, compression sensing method based on group wave conversion is substantially better than biography The compression sensing method based on wavelet transformation of system.

3. engineer applied example:

In order to verify the effectiveness of this invention proposition method further, test here, choose a width SAR image, figure As size is 256*256, carry out organizing wave conversion compressed sensing respectively and process and the process of wavelet transformation compressed sensing, to the weight obtained Composition picture carries out concrete relative analysis.Synthetic aperture radar be a kind of round-the-clock, round-the-clock can imaging radar, its imaging I.e. SAR image.The SAR image selected at this contains multiple target, such as road, bridge, waters and city etc., the figure that atural object is complicated As the effectiveness of the inventive method more can be described.

Fig. 9 is selected SAR image, and Figure 10 a, Figure 10 b are respectively group wave conversion compressed sensing and wavelet transformation compression The reconstruct image of perception.By Fig. 9 Yu Figure 10 a it can be seen that reconstruct image has substantially completely recovered the general picture of original image, texture is thin Joint is clear, and road, bridge, waters and urban architecture recovery situation are preferable.Figure 10 b is the fuzzyyest, and detail textures is covered substantially Lid, whole image blurring, especially upper left and bottom left section, review Figure 10 a then quality reconstruction good.From PSNR also Can be seen that, the PSNR of group ripple change compressed sensing reconstruct image is compared with the result of wavelet transformation compressed sensing much larger, it was demonstrated that group The remarkable advantage of wave conversion compression sensing method.

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Claims (1)

1. compression of images perception processing method based on group wave conversion, it is characterised in that: group wave conversion rarefaction representation is blended in In compressed sensing, detailed process is: first, image is carried out orthogonal systems wave conversion and obtains the sparse coefficient on all directions yardstick, Retain low frequency coefficient constant；Then, only it is compressed each yardstick high frequency coefficient measuring coding, requires to store for difference After transmission, compressed sensing restructing algorithm is used to recover high frequency coefficient；Finally, by the low frequency coefficient preserved and recovery High frequency coefficient carry out orthogonal systems ripple inverse transformation, thus the image being restored；

Said process is represented by following formula:；

Wherein:For organizing wave conversion base,Represent calculation matrix, primary signalAt group wave conversion baseEffect under be decomposed into There is the signal of K degree of rarefication；Measured value is obtained after measuring coding。