CN110113613B - Image block compressed sensing reconstruction method based on double sparse constraints of weight - Google Patents

Image block compressed sensing reconstruction method based on double sparse constraints of weight Download PDF

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CN110113613B
CN110113613B CN201910357504.1A CN201910357504A CN110113613B CN 110113613 B CN110113613 B CN 110113613B CN 201910357504 A CN201910357504 A CN 201910357504A CN 110113613 B CN110113613 B CN 110113613B
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仲元红
李琅
张静
马心怡
成欣雨
黄关
周昭坤
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Chongqing University
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Abstract

The invention discloses a method for compressing, sensing and reconstructing an image block based on dual sparse constraint of a reconstruction value, which comprises the following steps of: acquiring an observation signal; establishing a double sparse constraint image block compressed sensing reconstruction model based on a weight value; and solving a double sparse constraint image block compressed sensing reconstruction model based on the weight value based on an SBI algorithm to obtain an original signal corresponding to the observation signal. The method can better reconstruct the original image in a smooth area and an edge area, has obvious performance improvement and better visual effect compared with the prior art, and shows good stability and convergence. Work in the future includes image block matching optimization to reduce computational complexity, etc.

Description

Image block compressed sensing reconstruction method based on double sparse constraints of weight
Technical Field
The invention relates to the field of image processing, in particular to a method for compressing, sensing and reconstructing an image block based on dual sparse constraints of a reconstruction value.
Background
The compressed sensing theory aims at a series of problems of data transmission, data sampling and the like caused by the increasing of the information quantity, and provides a theory for recovering an original signal through a small amount of effective information. By directly collecting a small amount of important information in the information, the original signal can be recovered by using a sampling rate lower than the Nyquist theorem under the condition of ensuring that the information is not lost. The application of the compressive sensing theory can not only reduce the sampling rate and the data transmission cost, but also reduce the signal processing time, and the compressive sensing theory is rapidly developed in various fields in the last two decades and brings great convenience. Compressed sensing is also greatly applied to image processing, the data volume of image transmission is reduced, and the quality of reconstructed images is guaranteed.
The research on compressed sensing mainly comprises three aspects of research: (1) carrying out sparse transformation on the original signal under a group of orthogonal bases to generate a group of sparse signals; (2) designing an observation matrix, and acquiring an observation signal, namely a sampling signal, from the sparse signal through the observation matrix; (3) and recovering the original signal from the observation signal through a reconstruction algorithm. The premise of compressed sensing is sparseness of signals, and most of signal sparse representation methods are to transform non-sparse signals into sparse signals in a certain domain through Fourier transform, wavelet transform, discrete cosine transform, Gabor transform and the like. The observation matrix comprises a random Gaussian matrix, a random Bernoulli matrix, a Toeplitz matrix, a Hadamard matrix and the like. The signal reconstruction algorithm is the key point and difficulty of compressed sensing research, one type of reconstruction algorithm is a convex optimization algorithm based on 1-norm, the other type of reconstruction algorithm is a greedy algorithm based on 0-norm, and the method also comprises a combined algorithm.
In order to better reconstruct an original image in a smooth area and an edge area, the invention discloses a method for compressing, sensing and reconstructing an image block based on double sparse constraint of a weight value, which effectively utilizes the similarity between image blocks, constrains the noise influence by adding a regular term and the weight value, mathematically embodies a model into a problem of solving weighted 1-norm minimization and adopts an SBI framework to solve. Firstly, aiming at the proposed model, DCT (discrete cosine transform) is utilized to realize sparse representation of an original signal, random Gaussian projection is directly adopted as an observation matrix, then the model is converted from an unconstrained problem into a plurality of simple sub-problems under an SBI framework, and a steepest descent method and a soft threshold algorithm are utilized to solve the unconstrained problem through respectively solving the plurality of sub-problems, so that the original image is reconstructed. Compared with the prior art, the method has obvious performance improvement and better visual effect, and shows good stability and convergence. Work in the future includes image block matching optimization to reduce computational complexity, etc.
Disclosure of Invention
The invention discloses a method for image block compressed sensing reconstruction based on double sparse constraints of a weight value, which can better reconstruct an original image in a smooth region and an edge region. Work in the future includes image block matching optimization to reduce computational complexity, etc.
The invention adopts the following technical scheme:
the image block compressed sensing reconstruction method based on the double sparse constraints of the weight value comprises the following steps:
s101, acquiring an observation signal y;
s102, establishing a weight value-based double sparse constraint image block compressed sensing reconstruction model
Figure BDA0002045867340000021
Where x denotes the original signal, λ1And λ2All represent regularization constants, H represents an observation matrix, D represents the number of image blocks, xkRepresenting the kth image block, W1,kAnd W2,kAll represent xkWeight matrix of ukMeans representing similar image blocks;
s103, solving a double sparse constraint image block compressed sensing reconstruction model based on a weight value based on an SBI algorithm to obtain an original signal x corresponding to the observation signal y.
Preferably, the method further comprises the following steps:
observing signal y using MH reconstruction algorithmRecovering to obtain initial recovered signal xint；
Using matrix operators EkWill initially recover signal xintDivided into D overlapping image blocks, each block having a size S2。
Preferably, the first and second electrodes are formed of a metal,
Figure BDA0002045867340000022
c represents the number of most similar blocks, mk,iDenotes xkTo the ith most similar block, find mk,iThe method comprises the following steps:
at the initial recovery of signal xintIn xkSearch and x in a centered L sized search windowkTaking the C block with the highest similarity as xkMost similar block of (2), xkAnd mk,iDegree of similarity of
Figure BDA0002045867340000023
αk,iRepresents mk,iThe weight of (a) is calculated,
Figure BDA0002045867340000024
h is a constant.
Preferably, W1,kAnd W2,kIs a two-diagonal matrix with diagonal elements of
Figure BDA0002045867340000025
And
Figure BDA0002045867340000026
Figure BDA0002045867340000031
in summary, the invention discloses a reconstruction method for compressing and sensing an image block based on dual sparse constraint of a weight value, which comprises the following steps: acquiring an observation signal; establishing a double sparse constraint image block compressed sensing reconstruction model based on a weight value; and solving a double sparse constraint image block compressed sensing reconstruction model based on the weight value based on an SBI algorithm to obtain an original signal corresponding to the observation signal. The method can better reconstruct the original image in a smooth area and an edge area, has obvious performance improvement and better visual effect compared with the prior art, and shows good stability and convergence. Work in the future includes image block matching optimization to reduce computational complexity, etc.
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For purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made in detail to the present invention as illustrated in the accompanying drawings, in which:
FIG. 1 is a flowchart of a specific embodiment of a method for compressed sensing reconstruction of an image block based on dual sparse constraints of a weight value according to the present invention;
FIG. 2 is an experimental standard gray scale image in the present specification;
FIG. 3 is a schematic diagram of the complexity analysis of the experiment of the present invention;
FIG. 4 is a schematic diagram showing the comparison of the values of the number C of similar blocks to the reconstructed image in the experiment of the present invention;
in FIGS. 5(a) and 5(b), λ is1And λ2The performance of the reconstructed image is compared with the value of (1);
FIGS. 6(a) and 6(b) are schematic diagrams comparing the performance of the method of the present invention with a single regularization term algorithm;
FIG. 7 is a graph showing a comparison of the performance of h-valued reconstructed images;
fig. 8 to 13 are image comparison diagrams reconstructed by the method of the present invention and four other algorithms.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
As shown in FIG. 1, the invention discloses a reconstruction method for compressed sensing of an image block based on dual sparse constraint of a weight value, which comprises the following steps:
s101, acquiring an observation signal y;
s102, establishing a weight value-based double sparse constraint image block compressed sensing reconstruction model
Figure BDA0002045867340000032
Where x denotes the original signal, λ1And λ2All represent regularization constants, H represents an observation matrix, D represents the number of image blocks, xkRepresenting the kth image block, W1,kAnd W2,kAll represent xkWeight matrix of ukMeans representing similar image blocks;
s103, solving a double sparse constraint image block compressed sensing reconstruction model based on a weight value based on an SBI algorithm to obtain an original signal x corresponding to the observation signal y.
Since the application of the compressed sensing theory in the field of image processing, image reconstruction algorithms have gradually been widely learned and researched in the last two decades, and the purpose of the algorithm is to recover an original high-quality image x (original signal) from a degraded image y (observed signal). This is a typical inverse problem of morbidity, which can be summarized as:
y＝Hx+n
h denotes the observation matrix and n usually denotes additive gaussian noise. When H is the mask, the blurring operator and the gaussian random projection, respectively, y ═ Hx + n indicates image inpainting, image deblurring and compressed sensing problems.
To effectively solve the above inverse problem, image prior knowledge is typically employed to regularize the solution to the above problem to a minimization problem:
Figure BDA0002045867340000041
wherein
Figure BDA0002045867340000042
Is the 2-norm data fidelity term, Ψ (x) is the regularization term for the image prior, and λ is the regularization parameter. Various optimization methods have been proposed for the regularized image inverse problem described above.
The prior knowledge of the image has a crucial influence on the performance of an image reconstruction algorithm, so that the effective regular term is designed to be beneficial to accurately reflecting the image prior information in image recovery. The classical regularization term utilizes the local structure of the image and is established on the basis of local smoothness of the image except the edge, so that better performance can be embodied, but image details are generally ignored, and the image structure cannot be effectively processed.
The most important characteristics of an image are sparsity and non-local self-similarity. The non-local self-similarity describes the repeatability of a more complex pattern in an image, such as the texture and the structure of the image, and a non-local regularization term utilizing the non-local self-similarity of the image has a better effect than that of local regularization and has clearer image edges and detail parts, but the problem that the image details and the structure cannot be accurately restored still exists.
The invention discloses a method for compressing, sensing and reconstructing an image block based on dual sparse constraint of a reconstruction value, which comprises the following steps of: acquiring an observation signal; establishing a double sparse constraint image block compressed sensing reconstruction model based on a weight value; and solving a double sparse constraint image block compressed sensing reconstruction model based on the weight value based on an SBI algorithm to obtain an original signal corresponding to the observation signal. The method can better reconstruct the original image in a smooth area and an edge area, has obvious performance improvement and better visual effect compared with the prior art, and shows good stability and convergence. Work in the future includes image block matching optimization to reduce computational complexity, etc.
When the concrete implementation, still include:
recovering the observation signal y by MH reconstruction method to obtain an initial recovery signal xint；
Using matrix operators EkWill initially recover signal xintDivided into D overlapping image blocks, each block having a size S2。
In the specific implementation process, the first-stage reactor,
Figure BDA0002045867340000051
c represents the number of the most similar blocks,mk,idenotes xkTo the ith most similar block, find mk,iThe method comprises the following steps:
at the initial recovery of signal xintIn xkSearch and x in a centered L sized search windowkTaking the C block with the highest similarity as xkMost similar block of (2), xkAnd mk,iDegree of similarity of
Figure BDA0002045867340000052
αk,iRepresents mk,iThe weight of (a) is calculated,
Figure BDA0002045867340000053
h is a constant.
In the invention, when block processing is carried out, search and x are carried out in a search window with the size of L multiplied by LkOther images with similar information are matched and used to form a matrix in the Split Bregman Iteration (SBI) algorithm. For image blocks containing edges and singular points, noise has a small influence on useful information for determining the similarity between a target image block and a similar matching block of the target image block, but for a smooth area, because the pixel values of the target image block and the similar matching block are not greatly different, the noise plays a certain role in determining the matching process of the similar block, and therefore the noise may be stored in image information to influence image reconstruction.
xkResidual error x ofk-ukBy xkValue of (d) and its MH prediction mk,iThe value of the linear combination of 1. ltoreq. i.ltoreq.C can be expressed as,
xk-∑1≤i≤Cαk,imk,i
wherein alpha isk,iIs MH predicted mk,iThe purpose of which is to more directly represent the accuracy of MH predictions. When m isk,iAnd xkThe more similar, the greater the weight occupied, αk,iThe greater the value of (A); when m isk,iAnd xkThe smaller the similarity of (A), the smaller the occupied weight, alphak,iThe smaller the value of (c). Thus, αk,iAnd mk,iAnd xkThe similarity of (c) is inversely proportional. We calculate the similarity by Mean Square Error (MSE), which is expressed as:
Figure BDA0002045867340000054
wherein S2Is an image block xkThe size of (2).
Considering that the image blocks of the original image are unknown, we need to use the estimation of the image blocks
Figure BDA0002045867340000055
To calculate the weight alphak,i：
Figure BDA0002045867340000056
Where h is a constant. We can calculate the MH prediction mk,iCan effectively reflect MH prediction mk,iAnd image block
Figure BDA0002045867340000057
The similarity of (c).
In specific practice, W1，kAnd W2，kIs a two-diagonal matrix with diagonal elements of
Figure BDA0002045867340000058
And
Figure BDA0002045867340000059
Figure BDA00020458673400000510
each weight reflects the likelihood that the corresponding DCT coefficient goes to zero. The estimation value of the original image obtained by each iteration has better image quality than the last iteration result, so that the estimation value of the original image is close to the original image to a certain extent, and the original image can be effectively replaced to carry out iterative computation. The weight values are updated in each iteration, and the aim of obtaining better image restoration quality is fulfilled.
The image block compressed sensing reconstruction model based on the double sparse constraints of the weight value is converted into a plurality of simpler sub-problems by a variable separation technology from an unconstrained problem under an SBI framework by utilizing the idea based on an SBI algorithm, and then the problems are solved respectively. Optimizing a problem for a constraint
Figure BDA0002045867340000061
Wherein G ∈ RN×M,f:RN→R,g:RM→ R. For this form of constrained optimization problem, the SBI algorithm solution process is as follows:
Figure BDA0002045867340000062
in the SBI algorithm, the parameter μ is a fixed value. The SBI algorithm can decompose a complex problem into a plurality of sub-problems, the minimization solving of the sub-problems is much simpler than the minimization solving of the original problem, and the direct solving is realized
Figure BDA0002045867340000063
To a problem of (a).
First, the variable z needs to be introduced, and
Figure BDA0002045867340000064
conversion into an equivalent constraint expression of the same form
Figure BDA0002045867340000065
Then, based on the SBI algorithm, line 3 in algorithm 1 becomes:
Figure BDA0002045867340000066
line 4 in Algorithm 1 becomes:
Figure BDA0002045867340000071
line 5 in Algorithm 1 becomes:
b(t+1)＝b(t)-(z(t+1)-x(t+1))
where t represents the number of iterations and η is a fixed value parameter in SBI. Equation of
Figure BDA0002045867340000072
Has been converted into an equation by the SBI algorithm
Figure BDA0002045867340000073
Z sub-problem and an equation
Figure BDA0002045867340000074
The x sub-problem of (1).
The z sub-problem:
for a given x, the z sub-problem is a strictly convex quadratic function. In order to avoid calculating the inverse of the matrix and at the same time reduce the calculation amount of the algorithm, we use the steepest descent method (steeestDescent) to solve, and the equation is
Figure BDA0002045867340000075
The iterative formula of the steepest descent method is
z(t,i+1)＝z(t,i)-ρ(t,i)g(t,i)
Wherein g is(t,i)Denotes the gradient, p(t,i)Representing the optimal step size. t, i represent the number of iterations of the SBI algorithm and SD, respectively. Wherein the gradient and the optimal step length are calculated in the manner of
Figure BDA0002045867340000076
ρ＝gTg/gTQg
In the steepest descent method, we have
g(t,i)＝Qz(t,i)-b
Thus, we obtain
Q＝2HTH+η
Thereby obtaining
ρ＝gTg/gT(2HTH+η)g
Calculating the gradient and the optimal step length in the steepest descent method through the equation, performing i iterations in the internal loop of the SD, and putting the obtained z into an SBI algorithm to perform external loop updating.
Problem of x
For the case of a given z-value,
can be expressed as equation
Figure BDA0002045867340000081
Is rewritten as
Figure BDA0002045867340000082
Wherein r is(t)＝z(t+1)-b(t)。
During each iteration, we assume x, r(t)The difference between the elements of (a) satisfies the condition of the independent distribution with a mean value of zero. Thus, according to the Parceval's theorem, it is possible to obtain
Figure BDA0002045867340000083
Wherein K is DxS2。
Due to the orthogonality of DCT and Plancherel's theorem, one can obtain
Figure BDA0002045867340000084
Further obtain
Figure BDA0002045867340000085
Figure BDA0002045867340000086
It is broken down into sub-problems as follows:
Figure BDA0002045867340000087
convert it to a scalar problem, namely:
Figure BDA0002045867340000088
wherein, theta1＝Kλ1W1,k/Nη,θ2＝Kλ2W2,k/Nη，θ1,θ2Are known and are all constants, the scalars y, d, v, k corresponding to xk,r(t),x,ukFour vectors.
We get by soft threshold algorithm
Figure BDA0002045867340000089
Closed type solution of
Figure BDA00020458673400000810
Wherein S1(d)，S2(d) Are respectively as follows
Figure BDA0002045867340000091
Figure BDA0002045867340000092
X can be solved by the above formulakAnd pixel values of the corresponding image blocks at different positions can be calculated as expressed in
Figure BDA0002045867340000093
All image blocks x can be obtainedkK is more than or equal to 1 and less than or equal to D, and according to the mode of overlapping image blocks, the average value of all overlapped image blocks at a certain pixel point position can be calculated, so that an original image is reconstructed, and the reconstruction process can be carried out
Figure BDA0002045867340000094
The realization method is realized in the way that,
Figure BDA0002045867340000095
is an observation matrix.
Having solved the z and x sub-problems, we proceed through equation b(t+1)＝b(t)-(z(t+1)-x(t+1)) And b is updated, and the three steps are repeated until all the iterative processes are finished. To this end, all the problems of compressed perceptual reconstruction models with multiple constraints have been solved under the framework of SBI algorithms. The algorithm for solving the image block compressed sensing reconstruction model based on the double sparse constraint of the weight value is as follows:
Figure BDA0002045867340000096
Figure BDA0002045867340000101
Figure BDA0002045867340000102
i.e. the reconstructed map obtained after all iterationsFor example, the following is a verification of the performance of the method of the present invention by experiment, and the model parameters are set as follows: when the original image is compressed and sensed, the size B of the image block is 64. The width of the overlap between adjacent image blocks is 4 pixels. The window size L × L is 20 × 20, and the remaining parameters will be described in detail below after testing. All experiments were performed on MATLAB 2012b of the Intel (R) Core (TM) i3, CPU processor at 3.0GHz, Windows 10 operating system.
To evaluate the quality of the reconstructed image, we used the peak signal-to-noise ratio (PSNR) and Structural Similarity (SSIM), which are commonly used for objective evaluation of image quality. A higher PSNR means a better quality of reconstruction and the original image is clearly reconstructed. A lower PSNR indicates a poor quality of reconstruction and problems such as edge blurring exist. SSIM is used to reflect the similarity between the original image and the reconstructed image in the structure. Experimental results show that the PSNR and SSIM of the image are reconstructed by the algorithm and the other four algorithms. All experimental standard gray scale images are shown in fig. 2.
The larger search window can find xkMore similar blocks, and thus a more accurate model can be obtained. However, it also brings with it a higher computational complexity. In the experiment, we tested the computation time for different scales of images. As shown in fig. 3, we demonstrate the algorithm complexity for different search window sizes L.
In order to test the influence of the number of similar blocks, different pictures are tested by adopting different numbers of similar blocks. It can be seen from the experimental results of fig. 4 that the method of the present invention is insensitive to the number of similar blocks, since all curves are close to flat. The number of similar blocks shows a certain degree of similarity for different images. According to extensive experimental results, all test images achieved the highest and most stable performance when C was 10. Therefore, the value of C is 8-10, so that the stability can be obtained and the computational complexity is reduced.
To study the effect of regularization parameters on performance, we needed to test their different values separately. Lambda [ alpha ]1And λ2The performance of the model is affected, therefore, a parameter needs to be determined and measuredOther parameters are tried. As can be seen from FIGS. 5(a) and 5(b), if λ1And λ2Too large or too small an amplitude will affect the image reconstruction performance. Also, for different images, λ1And λ2The effect on PSNR shows consistency, which means that there are optimal regularization parameters, which make the performance of the algorithm optimal under different image conditions. In the experiment, we set λ12.5e-3 and λ2＝2.5e-4。
To verify the high performance of the method of the invention, let λ be assumed1And λ2The values are set to zero, respectively. The results of the experiment are shown in fig. 6(a) and 6 (b). For different images, the PSNR of the image reconstructed by a separate sparse constraint term is slightly lower than that of the image reconstructed by the present invention, i.e. the performance of the model proposed by the present invention, which combines non-local similarity and local self-similarity, is superior to the performance of the model which utilizes non-local sparsity and local self-similarity, respectively. The model proposed by the present invention achieves the highest PSNR. For ship images, the PSNR of the method of the invention is improved by 0.01dB and 1dB compared with a single sparse constraint model. For the Lena image in the figure, the PSNR of the proposed algorithm is typically improved by 0.06dB and 0.4dB compared to the sparse constraint model alone.
αk,iThe parameter value h in (2) affects the accuracy of the similar block and further affects the performance of the reconstructed image. Therefore, we take values of 1 to 120 for h to test the reconstruction performance. A number of experiments were performed under three images. As can be seen from fig. 7, the parameter values have some influence on the quality of the reconstructed image. PSNR shows a certain stability and reaches a maximum in the range of 70 to 120. Different test images show consistency, i.e. different reconstructed images can achieve the best reconstruction performance in the same range. Therefore, in the present invention, the experimental value is h 80.
The observation signal y is obtained by applying a gaussian random projection matrix to the original image. We propose four representative compressed sensing reconstruction algorithms and the method (deployed) reconstruction results of the present invention, including BCS-SPL-DCT and BCS-SPL-DWT, MH method and cooperative sparsity (CoS) method. Notably, the MH method and the CoS method are considered as advanced algorithms in the reconstruction of the image CS. We show the PSNR/SSIM of the reconstructed images in the following table.
Figure BDA0002045867340000111
Figure BDA0002045867340000121
The image reconstructed by the proposed algorithm is visually compared with the images reconstructed by the other four algorithms. The comparison results are shown in fig. 8 to 13.
FIG. 8: at a ratio of 20%, the performance of pictures reconstructed by compressed sensing of gray images Goldhill under different reconstruction algorithms were compared. From left to right in sequence: original image, image reconstructed by MH, image reconstructed by BCS-SPL-DCT, image reconstructed by BCS-SPL-DWT, image reconstructed by CoS, image reconstructed by the algorithms herein.
FIG. 9: at a ratio of 20%, the performance of pictures reconstructed by compressed sensing of the gray image Barbara under different reconstruction algorithms were compared. From left to right in sequence: original image, image reconstructed by MH, image reconstructed by BCS-SPL-DCT, image reconstructed by BCS-SPL-DWT, image reconstructed by CoS, image reconstructed by the algorithms herein.
FIG. 10: at a ratio of 30%, the performance of pictures reconstructed by compressed sensing of gray image Cameraman under different reconstruction algorithms were compared. From left to right in sequence: original image, image reconstructed by MH, image reconstructed by BCS-SPL-DCT, image reconstructed by BCS-SPL-DWT, image reconstructed by CoS, image reconstructed by the algorithms herein.
FIG. 11: at a ratio of 30%, the performance of pictures reconstructed by compressed sensing of the gray image Boat under different reconstruction algorithms were compared. From left to right in sequence: original image, image reconstructed by MH, image reconstructed by BCS-SPL-DCT, image reconstructed by BCS-SPL-DWT, image reconstructed by CoS, image reconstructed by the algorithms herein.
FIG. 12: at a ratio of 40%, the performance of pictures reconstructed by compressed sensing of gray image Lena under different reconstruction algorithms were compared. From left to right in sequence: original image, image reconstructed by MH, image reconstructed by BCS-SPL-DCT, image reconstructed by BCS-SPL-DWT, image reconstructed by CoS, image reconstructed by the algorithms herein.
FIG. 13: at a ratio of 40%, the performances of pictures reconstructed by compressed sensing of gray image Peppers under different reconstruction algorithms were compared. From left to right in sequence: original image, image reconstructed by MH, image reconstructed by BCS-SPL-DCT, image reconstructed by BCS-SPL-DWT, image reconstructed by CoS, image reconstructed by the algorithms herein.
These figures show the PSNR and SSIM of images reconstructed by different reconstruction algorithms at a rate of 20%, 30% and 40%. According to experimental results, images reconstructed by BCS-SPL-DCT and BCS-SPL-DWT are generally fuzzy, the texture structure is not clear enough, and the visual effect is poorer than that of the other three algorithms. The images reconstructed by the MH algorithm and the CoS algorithm both have better image quality and the visual intuition effect is not much different. In particular, the CoS algorithm reconstructs images with stronger texture and higher quality. In the aspect of PSNR, the image reconstructed by the method is slightly higher than the image reconstructed by an MH algorithm and a CoS algorithm, namely the image reconstruction quality can be effectively improved by the algorithm provided by the invention, and the algorithm is generally better than the four classic compressed sensing reconstruction algorithms.
Finally, it is noted that the above-mentioned embodiments illustrate rather than limit the invention, and that, while the invention has been described with reference to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (1)

1. The image block compressed sensing reconstruction method based on the double sparse constraints of the weight value is characterized by comprising the following steps of:
s101, acquiring an observation signal y;
recovering the observation signal y by using MH reconstruction algorithm to obtain an initial recovery signal xint；
Using matrix operators EkWill initially recover signal xintDivided into D overlapping image blocks, each block having a size S2；
S102, establishing a weight value-based double sparse constraint image block compressed sensing reconstruction model
Figure FDA0002731351390000011
Where x denotes the original signal, λ1And λ2All represent regularization constants, H represents an observation matrix, D represents the number of image blocks, xkRepresenting the kth image block, W1,kAnd W2,kAll represent xkWeight matrix of ukMeans representing similar image blocks;
Figure FDA0002731351390000012
c represents the number of most similar blocks, mk,iDenotes xkTo the ith most similar block, find mk,iThe method comprises the following steps:
at the initial recovery of signal xintIn xkSearch and x in a centered L sized search windowkTaking the C block with the highest similarity as xkMost similar block of (2), xkAnd mk,iDegree of similarity of
Figure FDA0002731351390000013
αk,iRepresents mk,iThe weight of (a) is calculated,
Figure FDA0002731351390000014
h is a constant;
W1,kand W2,kIs a two-diagonal matrix with the elements on the diagonals being wk,1，wk,2，wk,3，...，
Figure FDA0002731351390000015
And
Figure FDA0002731351390000016
Figure FDA0002731351390000017
Figure FDA0002731351390000018
s103, solving a double sparse constraint image block compressed sensing reconstruction model based on a weight value based on an SBI algorithm to obtain an original signal x corresponding to the observation signal y.
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