CN108093266B - image compressed sensing reconstruction system and method using group normalization sparse representation - Google Patents

Abstract

the invention discloses an image compressed sensing reconstruction system and method by using group normalization sparse representation, and relates to the technical field of image recovery. The system comprises an initialization module (1), a routing selection module (2), a regularized mean square error minimum module (3) and an image filtering processing module (4); the initialization module (1), the routing module (2), the regularized mean square error minimum module (3) and the image filtering processing module (4) are sequentially interacted, and the image filtering processing module (4) is interacted with the routing module (2). The method can improve the recovery effect of the small and weak target, the texture and the edge of the image, and effectively improve the reconstruction quality of the compressed sensing image; suitable for compression imaging applications.

Description

image compressed sensing reconstruction system and method using group normalization sparse representation

Technical Field

The invention relates to the technical field of image recovery, in particular to an image compressed sensing reconstruction system and method by using group normalization sparse representation.

background

as a new signal sampling theory proposed in recent years, the Compressed Sensing (CS) sampling theory breaks through the constraint of the conventional nyquist sampling theory, and can realize accurate reconstruction of sparse signal dimension reduction sampling. This theory has been drawing attention in the fields of signal sensing, image processing, wireless communication, and the like since its introduction and has begun to be applied. The image compressed sensing has wide application prospect in the fields of remote sensing images, medical imaging and the like, and the high-quality reconstruction of the compressed sensing images is the key point of the successful application of the compressed sensing images.

In order to realize accurate reconstruction of the compressed sensing signal and better improve reconstruction performance, it is very important to find sparse representation suitable for sampling signals; however, for the compressed perceptual reconstruction of image signals, how to fully utilize the local similarity and non-local similarity of image signals to better enhance the sparse representation capability of images, thereby further effectively enhancing the image reconstruction quality, is an important direction that researchers In this field have been concerned In recent years, such as the method based on total variation [1] Li C, Yin W, Zhang y.tval3: TV minor added orientation algorithms [ EB/OL ].2013. http:// www.caam.rice.edu/optimization/L1/TVAL 3], the method based on multiple assumptions [2] CHEN C, TRAMEL E w.compressed-sensing approach of images and video using multiple-locations [ C ]/In front, 45fifth, related, non-local similarity [ n ] 3, USA-3, and "n + 3, C-3, b-C, 3, b-C, C-45fifth, 3, C, b-C, b-3, b-C, b-C, b, ZHao D, Gao W.Group-based sparse representation for Image retrieval [ J ]. IEEE Transactions on Image Processing,2014,23(8): 3336-.

however, in most conventional methods, the sparsity of the image signal after some kind of transformation is simply used to constrain the reconstruction, so that the tiny and important detail information existing in the image is lost, and a satisfactory reconstruction effect is difficult to obtain.

Disclosure of Invention

the invention aims to overcome the defects of the background technology, and provides an image compressed sensing reconstruction system and method using group normalization sparse representation, which can better retain detailed information of small and weak targets, textures, edges and the like of an image, thereby effectively improving the quality of the reconstructed image.

the technical idea of the invention is as follows:

firstly, obtaining an initial estimation value of compressed sensing image reconstruction by adopting an image compressed sensing reconstruction method; then, the mean value removing normalization of different sub-band coefficients of the block image is used for expressing the prior with approximate consistent statistical distribution, and the reconstruction quality of the compressed sensing image is effectively improved through multiple iterations and mean value removing soft threshold filtering processing by using an image block group PCA transformation domain.

image compressed sensing reconstruction system (system for short) by using group normalization sparse representation

The system comprises an initialization module, a routing module, a regularized mean square error minimum module and an image filtering processing module;

the initialization module, the routing module, the regularized mean square error minimum module and the image filtering processing module are sequentially interacted, and the image filtering processing module is interacted with the routing module.

image compressed sensing reconstruction method (method for short) by using group normalization sparse representation

the method comprises the following steps:

firstly, an initialization module receives a compressed sampling value y of an input image, generates an initial estimation value z of compressed sensing image reconstruction by adopting a compressed sensing image reconstruction method, and sends the initial estimation value z to a routing module, and initially sets a Brahman distance a to be 0, an iteration time t to be 0, a maximum iteration time J, and regularization parameters lambda and mu;

the regularization mean square error minimum module obtains an estimated value x of a reconstructed image through solving according to an estimated value z of compressed sensing image reconstruction input by the routing module and a compressed sampling value y of an input image, and sends the estimated value x to the image filtering processing module; phi is a measurement matrix, usually selected as a random matrix, and a is a Brazilian distance;

Thirdly, the image filtering processing module carries out mean value removing soft threshold filtering processing based on a transform domain coefficient level on the primary updated estimated value x of the reconstructed image input by the regularized mean square error minimum module to obtain a secondary updated estimated value z of the reconstructed image;

Updating the Brahman distance a: a ═ a- (x-z), and the updating iteration time t ═ t + 1; if the iteration time t is not more than the set maximum iteration time J, returning to the step II; otherwise, executing the fifth step;

and fifthly, finishing the operation and outputting the finally obtained reconstructed image z.

the working mechanism is as follows:

the invention is generally implemented in two stages:

the first stage, an initial estimation value of compressed sensing image reconstruction is obtained by adopting an image compressed sensing reconstruction method;

And in the second stage, the prior with approximate consistent statistical distribution is represented by using the mean value removal normalization of different sub-band coefficients of the block images of the images, the group normalization sparse representation regularization optimization is adopted, and the quality of the compressed sensing image reconstruction is improved through multiple iterations, wherein the iterations comprise two processes: the first process is that according to the compression sampling value of the known image, the estimation value of the reconstructed image is updated once by adopting a regularization mean square error minimum method; and the second process is to perform secondary updating on the estimated value of the reconstructed image by adopting an image similarity block group transform domain mean value removing soft threshold filtering method according to the estimated value of the reconstructed image which is updated once.

compared with the prior art, the invention has the following advantages and positive effects:

The method can improve the recovery effect of the small and weak target, the texture and the edge of the image, and effectively improve the reconstruction quality of the compressed sensing image; suitable for compression imaging applications.

drawings

FIG. 1 is a block diagram of the architecture of the present system;

in the figure:

1-an initialization module;

2-routing module;

3-regularized mean square error minimum module;

4-an image filtering processing module for processing the image,

401-the image is overlapped by a block unit,

402-an image similarity block group generating unit,

403-transform domain de-averaging soft threshold filtering unit,

And 404, an image block pixel domain averaging unit.

figure 2.1 is the original image for the experiment,

figure 2.2 is a reconstructed image using the document [2] method,

figure 2.3 is a reconstructed image using the method of document 3,

fig. 2.4 is a reconstructed image using the method of the invention.

Detailed Description

the following detailed description is made with reference to the accompanying drawings and examples:

a, system

1. General of

As shown in fig. 1, the system includes an initialization module 1, a routing module 2, a regularized mean square error minimization module 3 and an image filtering processing module 4;

the initialization module 1, the route selection module 2, the regularized mean square error minimum module 3 and the image filtering processing module 4 are sequentially interacted, and the image filtering processing module 4 and the route selection module 2 are interacted.

In detail: the routing module 2 has two input ends and one output end, and the regularized mean square error minimum module 3 has 2 input ends and 1 output end; one input end of the routing module 2 interacts with the output end of the initialization module 1, the other input end of the routing module 2 interacts with the output end of the image block pixel domain averaging unit 404, one input end of the regularized mean square error minimum module 3 interacts with the system input end, the other input end interacts with the output end of the routing module 2, the output end of the regularized mean square error minimum module 3 interacts with the input end of the image overlap block unit 401, an output of the image overlap blocking unit 401 interacts with an input of the image similarity block group generating unit 402, the output of the image similarity block group generating unit 402 interacts with the input of the transform domain de-averaging soft threshold filtering unit 403, the output of the transform domain de-averaging soft threshold filtering unit 403 interacts with the input of the image block pixel domain averaging unit 404, the output end of the image block pixel domain averaging unit 404 is the output end of the image compressed sensing reconstruction system.

2. Functional module

1) Initialization Module 1

The initialization module 1 receives compressed sampling values of an input image, and obtains an initial estimation value of compressed sensing image reconstruction by using a conventional image compressed sensing reconstruction method such as a multi-hypothesis method (more other similar methods can be used) proposed in document [3], and sends the initial estimation value to the routing module 2.

2) Routing module 2

the routing module 2 outputs the initial estimation value of the compressed sensing image reconstruction sent by the initialization module 1 for the first time, and then outputs the updated estimation value of the compressed sensing image reconstruction sent by the image block pixel domain averaging unit 404.

3) Regularized mean square error minimum module 3

the regularization mean square error minimum module 3 obtains an estimated value of one-time updating of the reconstructed image according to the estimated value of the image reconstruction sent by the routing module 2 and the compression sampling value of the input image. Specifically, the method is obtained by taking the derivative of the function with respect to the variable x to be equal to zero, or by using a gradient descent method to iteratively solve.

4) image filtering processing module 4

The image filtering processing module 4 comprises an image overlapping block unit 401, an image similar block group generating unit 402, a transform domain mean value removing soft threshold filtering unit 403 and an image block pixel domain averaging unit 404 which are sequentially interacted;

(1) Image overlap blocking unit 401

the image overlapping and blocking unit 401 performs overlapping and blocking on the image output by the regularized mean square error minimum module 3 to obtain a plurality of image blocks with overlapped pixels, and sends the image blocks into the image similar block group generating unit 402;

(2) Image similarity block group generating unit 402

the image similar block group generating unit 402 finds a group of similar image blocks in a specified neighborhood range of an image in which each image block sent by the image overlapping block 401 unit is located, vectorizes the group of similar image blocks to generate a data matrix corresponding to the image block, and sends the data matrix to the transform domain mean value removing soft threshold filtering unit 403;

(3) Transform domain de-averaging soft threshold filtering unit 403

the transform domain mean removing soft threshold filtering unit 403 generates 402 each data matrix sent by the unit for generating image similar block groups, generates a PCA transform dictionary according to the covariance matrix thereof, multiplies the transform dictionary with the data matrix to obtain a transform domain coefficient matrix, then obtains the mean and variance of each sub-band corresponding to the transform domain coefficient matrix, further performs mean removing soft threshold shrinking processing on each coefficient of the transform domain according to the difference of the sub-band to which the coefficient belongs, multiplies the transform domain coefficient matrix of the inverse transform dictionary with the soft threshold shrinking processing, and sends the result to the image block pixel domain averaging unit 404;

(4) Image block pixel domain averaging unit 404

the image block pixel domain averaging unit 404 calculates weighted average of corresponding pixels in the pixel domain for the data matrix sent by the transform domain de-averaging soft threshold filtering unit 403 to obtain a secondary updated estimation value of the reconstructed image; and then the estimated value of the secondary update is sent to a routing module 2, the routing module 2 sends the estimated value of the secondary update to a regularized mean square error minimum module 3, and iterative operation is continued to achieve the purpose of gradually improving the quality of the output image.

second, method

1. The method comprises the following steps:

The reconstruction method of the compressed sensing image comprises the following steps:

A. Solving a sparse coefficient eta of a compression sampling value y of an input image under a sparse dictionary D into an adjustable regularization parameter, wherein the sparse dictionary D can be discrete cosine transform, discrete wavelet transform or a dictionary based on learning;

B. Multiplying the sparse coefficient by a sparse dictionary D to obtain an initial estimated value z of image reconstruction, wherein the initial estimated value z is as follows:

2. Step three:

a. An image overlapping and blocking unit (401) of the image filtering processing module (4) receives the image x output by the regularized mean square error minimum module (3), performs overlapping and blocking on the x to obtain a plurality of image blocks xi with pixel overlapping, and sends the image blocks xi into an image similar block group generating unit (402); image blocks xi ═ Ri (x), i ═ 1,2, … n, n is an integer greater than 2, and represents the total number of image blocks, Ri (·) represents an operation matrix for extracting the ith image block, and the size of the image block is generally selected to be B ═ 8 rows × 8 columns;

b. the image similar block group generating unit (402) calculates m-1 most similar image blocks of each image block xi sent by the image overlapping and blocking unit (401) in a specified neighborhood window of an image x where the image block xi is located, wherein m is a positive integer between 40 and 60, and the size of the neighborhood window is 40 multiplied by 40; vectorizing the image block and similar image blocks thereof to generate a data matrix Ai corresponding to the image block, and sending the data matrix Ai into a transform domain mean value removing soft threshold filtering unit (403); the data matrix represents a matrix formed by the extracted ith image block and the similar blocks thereof and is an operation matrix of the similar block group for extracting the ith image block;

c. for each data matrix Ai sent by the image similarity block group generating unit (402), a transform domain mean value removing soft threshold filtering unit (403) firstly generates a Principal Component Analysis (PCA) transform dictionary Ψ according to a covariance matrix of the data matrix Ai; then multiplying the transformation dictionary psi with the data matrix Ai to obtain an Ai transformation domain coefficient alpha i; then correspondingly calculating a mean value zeta i and a variance sigma i of the alpha i according to the sub-bands, calculating a threshold value, and further performing threshold value contraction processing on the coefficient alpha i; finally, the coefficient obtained after the threshold contraction processing is inversely transformed, and the obtained data matrix after the filtering processing is sent to an image block pixel domain averaging unit (404); where./denotes a point division operation at the element level, # denotes a point multiplication operation at the element level, sgn (·) denotes a symbol extraction operation at the element level, max (·) denotes a maximum value taking operation, abs (·) denotes an absolute value taking operation at the element level, epsilon is a non-zero micro constant that avoids calculation overflow, Ψ -1 denotes an inverse matrix of Ψ, and N is the dimension of the original image;

d. An image block pixel domain averaging unit (404) calculates all data matrixes i which are sent by a transform domain de-averaging soft threshold filtering unit (403) to obtain a secondary updated estimated value z of a reconstructed image, and sends the estimated value z to a routing module (2); where R' Ai is the transpose of RAi, 1B m is a matrix of size B m with element value 1, B m is the dimension of the matrix.

Third, simulation experiment

to prove the effectiveness of the embodiments of the present invention, the applicant performed simulation experiments under the MATLAB platform. 2.1-2.4 show the subjective visual effect of the reconstructed image of the present invention compared with the methods of documents [2], [3] at a sampling rate set to 0.1, the test image being a 256 × 256Boats image; fig. 2.1 is an original image for experiment, fig. 2.2 is a reconstructed image by the method of document [2], fig. 2.3 is a reconstructed image by the method of document [3], and fig. 2.4 is a reconstructed image by the method of the present invention. In the experiment, a compressed sensing measurement matrix adopts a random projection matrix; setting the size of an image block of an image overlapping block to be 8 multiplied by 8 and the interval between blocks to be 4; in the extraction of the similar image block group, the size of the structurally similar image block group is set to be m 60, the window size for searching the similar block is 40 × 40, and the regularization parameter λ is set to be 0.09, and μ is set to be 0.0025.

Claims (1)

1. an image compressed sensing reconstruction method using group normalization sparse representation comprises the following steps:

firstly, an initialization module (1) receives a compressed sampling value y of an input image, generates an initial estimation value z of compressed sensing image reconstruction by adopting a compressed sensing image reconstruction method, and sends the initial estimation value z to a routing selection module (2), and initially sets a Blackerman distance a to be 0, an iteration time t to be 0, a maximum iteration time J, and regularization parameters lambda and mu;

The regularization mean square error minimum module (3) obtains an estimated value x of a reconstructed image through solving according to an estimated value z of compressed sensing image reconstruction input by the routing module (2) and a compressed sampling value y of an input image, and sends the estimated value x to the image filtering processing module (4); phi is a measurement matrix, usually selected as a random matrix, and a is a Brazilian distance;

The image filtering processing module (4) carries out filtering processing on the primary updated estimated value x of the reconstructed image input by the regularized mean square error minimum module (3) to obtain a secondary updated estimated value z of the reconstructed image;

Updating the Brahman distance a: a ═ a- (x-z), and the updating iteration time t ═ t + 1; if the iteration time t is not more than the set maximum iteration time J, returning to the step II; otherwise, executing the fifth step;

Fifthly, finishing the operation and outputting the finally obtained reconstructed image z;

the steps are as follows:

The reconstruction method of the compressed sensing image comprises the following steps:

A. solving a sparse coefficient eta of a compression sampling value y of an input image under a sparse dictionary D into an adjustable regularization parameter, wherein the sparse dictionary D can be discrete cosine transform, discrete wavelet transform or a dictionary based on learning;

B. multiplying the sparse coefficient by a sparse dictionary D to obtain an initial estimated value z of image reconstruction, wherein the initial estimated value z is as follows:

the method is characterized in that:

The third step is that:

a. An image overlapping and blocking unit (401) of the image filtering processing module (4) receives the image x output by the regularized mean square error minimum module (3), performs overlapping and blocking on the x to obtain a plurality of image blocks xi with pixel overlapping, and sends the image blocks xi into an image similar block group generating unit (402); image blocks xi ═ Ri (x), i ═ 1,2, … n, n is an integer greater than 2, and represents the total number of image blocks, Ri (·) represents an operation matrix for extracting the ith image block, and the size of the image block is generally selected to be B ═ 8 rows × 8 columns;

b. the image similar block group generating unit (402) calculates m-1 most similar image blocks of each image block xi sent by the image overlapping and blocking unit (401) in a specified neighborhood window of an image x where the image block xi is located, wherein m is a positive integer between 40 and 60, and the size of the neighborhood window is 40 multiplied by 40; vectorizing the image block and similar image blocks thereof to generate a data matrix Ai corresponding to the image block, and sending the data matrix Ai into a transform domain mean value removing soft threshold filtering unit (403); the data matrix represents a matrix formed by the extracted ith image block and the similar blocks thereof and is an operation matrix of the similar block group for extracting the ith image block;

c. For each data matrix Ai sent by the image similarity block group generating unit (402), a transform domain mean value removing soft threshold filtering unit (403) firstly generates a Principal Component Analysis (PCA) transform dictionary Ψ according to a covariance matrix of the data matrix Ai; then multiplying the transformation dictionary psi with the data matrix Ai to obtain an Ai transformation domain coefficient alpha i; then correspondingly calculating a mean value zeta i and a variance sigma i of the alpha i according to the sub-bands, calculating a threshold value, and further performing threshold value contraction processing on the coefficient alpha i; finally, the coefficient obtained after the threshold contraction processing is inversely transformed, and the obtained data matrix after the filtering processing is sent to an image block pixel domain averaging unit (404); where./denotes a point division operation at the element level, # denotes a point multiplication operation at the element level, sgn (·) denotes a symbol extraction operation at the element level, max (·) denotes a maximum value taking operation, abs (·) denotes an absolute value taking operation at the element level, epsilon is a non-zero micro constant that avoids calculation overflow, Ψ -1 denotes an inverse matrix of Ψ, and N is the dimension of the original image;

d. An image block pixel domain averaging unit (404) calculates all data matrixes i which are sent by a transform domain de-averaging soft threshold filtering unit (403) to obtain a secondary updated estimated value z of a reconstructed image, and sends the estimated value z to a routing module (2); where R' Ai is the transpose of RAi, 1B m is a matrix of size B m with element value 1, B m is the dimension of the matrix.