CN113222861A - Image recovery method and system based on equality structure multiple regularization - Google Patents

Image recovery method and system based on equality structure multiple regularization Download PDF

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CN113222861A
CN113222861A CN202110615237.0A CN202110615237A CN113222861A CN 113222861 A CN113222861 A CN 113222861A CN 202110615237 A CN202110615237 A CN 202110615237A CN 113222861 A CN113222861 A CN 113222861A
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CN113222861B (en
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郭企嘉
辛志男
周天
李海森
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Harbin Engineering University
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Abstract

The invention discloses an image recovery method and system based on equality structure multiple regularization, wherein an equality structure is introduced to construct a measurement Gaussian likelihood function; selecting a plurality of sparse transformations based on the constructed measurement Gaussian likelihood function, and giving a plurality of probability density functions which are independent to each other on the basis of sparse transformation coefficients to calculate the conditional prior probability density of the target image; calculating a mean value estimation model of the target image according to a Bayes rule based on the conditional prior probability density of the target image; and finally, combining an expectation maximization method with a conjugate gradient method to iteratively realize the rapid reconstruction of a target image, overcoming the reversibility limitation of introducing sparse representation by a comprehensive method, allowing any number of sparse transformations to be adopted, and effectively improving the convergence rate of the algorithm by combining a sparse domain.

Description

Image recovery method and system based on equality structure multiple regularization
Technical Field
The invention belongs to the field of image restoration, and particularly relates to an image restoration method and system based on equation structure multiple regularization.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
Compressed Sensing (CS), as a sparse reconstruction technique, is currently widely used in various fields, such as radar and medical imaging, seismic imaging, image processing, and the like. According to the CS theory, on the premise that the signal meets the sparsity requirement, the original signal can be reconstructed with high precision through sampling data volume which is far smaller than the requirement of the Nyquist-Shannon sampling law. But it is more noticeable that the CS also has excellent performance in terms of high-precision reconstruction and estimation of the signal. In order to take reconstruction precision of sparse signals and solving difficulty of CS problem into consideration, greedy method is often adopted for approximate solution, or l of original CS is used0Norm-optimized relaxation to l1The optimization problem is solved, called LASSO. The solving methods have good solving efficiency, but the sparse reconstruction performance of the signals cannot be guaranteed.
The Bayesian Compressive Sensing (BCS) method can effectively improve the reconstruction performance of the sparse signal, and does not need a user to define important regularization parameters and provide an uncertainty estimation result. BCS is reported to have higher reconstruction success rate and lower Normalized Mean Square Error (NMSE) under severe conditions of low sampling rate, high sparsity of signal and low signal-to-noise ratio relative to CS. Accordingly, BCS is increasingly being used for high resolution beamforming, imaging, and image recovery algorithms. However, for complex images, the target to be reconstructed does not have sparsity, and the image reconstructed directly through the CS or BCS cannot meet the sparsity requirement, so that the reconstruction accuracy is greatly reduced.
In the image recovery method, the recovery success rate and the image quality of an image can be effectively improved by combining a regularization sparse representation method, the principle is that an original optimization problem is converted into a norm optimization problem of a sparse representation coefficient, the sparse coefficient is reconstructed on the premise that the image is known to have sparsity in a specific sparse representation domain, and then the original image is recovered. Common sparse representation methods include Total Variation (TV) and its variants, discrete cosine transform, wavelet transform, shear wave transform, etc. Various methods have respective advantages, but for complex images, it is difficult to ensure that the optimal sparse representation is obtained through a certain regularization transformation. By using multiple sparse representations simultaneously, namely multiple regularization, the sparse representation capability can be effectively improved. Combining the CS Method with multiple regularization is not difficult to expand on the original CS solution methods, such as Alternating Direction Method of Multipliers (ADMM), optimization minimization (MM), and Proximity Method (PM).
However, when the original BCS is solved, a conjugate matching relationship must be established through a target prior probability hypothesis, then all probability parameters are calculated through bayesian inference, and a mean value and a covariance matrix of an image are estimated in iteration. The single sparse transform can be realized by modifying a linear model through a synthesis method, but the synthesis method cannot be used for irreversible sparse transform or multiple sparse transforms. Therefore, in the field of complex image recovery algorithms, a multiple regularization BCS method with complete theoretical basis and wide applicability does not appear yet.
Disclosure of Invention
The invention aims to solve the problems, provides an image recovery method and system based on equality structure multiple regularization, introduces a plurality of sparse transformations through the equality structure, namely introduces a plurality of independent Delta probability density functions, establishes a multi-level Bayes model with multiple limits through Bayes law, gives sparse hypothesis to transformation coefficients corresponding to each transformation, thereby establishes conjugate matching relation among each hierarchy, and finally realizes rapid reconstruction of a target image through an expectation maximization method combined with conjugate gradient method iteration.
According to some embodiments, the invention adopts the following technical scheme:
the image restoration method based on the equation structure multiple regularization comprises the following steps:
after receiving an image to be restored, converting the image into a one-dimensional signal, and projecting the one-dimensional signal to an observation vector by using a measurement matrix;
inputting the measurement matrix and the observation vector into an image recovery model based on multiple regularization of an equality structure to obtain a target image mean value; the image restoration model calculates the mean value and the intermediate variable of the target image by adopting a conjugate gradient method according to the measurement matrix and the observation vector; updating the hyperparametric vector and the equality variance of Bayesian compressed sensing by using the intermediate variable and the target image mean value obtained by calculation; judging whether a convergence condition is met, and if so, outputting a target image mean value; and otherwise, returning to recalculate the mean value and the intermediate variable of the target image by using the updated hyper-parameter vector and equation variance.
An image restoration system based on multiple regularization of an equation structure, comprising:
the image receiving module is used for receiving the image to be recovered, converting the image into a one-dimensional signal and projecting the one-dimensional signal to an observation vector by using a measurement matrix;
the image restoration module is used for inputting the measurement matrix and the observation vector into an image restoration model based on multiple regularization of an equation structure to obtain a target image mean value; the image restoration model calculates the mean value and the intermediate variable of the target image by adopting a conjugate gradient method according to the measurement matrix and the observation vector; updating the hyperparametric vector and the equality variance of Bayesian compressed sensing by using the intermediate variable and the target image mean value obtained by calculation; judging whether a convergence condition is met, and if so, outputting a target image mean value; and otherwise, returning to recalculate the mean value and the intermediate variable of the target image by using the updated hyper-parameter vector and equation variance.
An electronic device comprising a memory and a processor, and computer instructions stored on the memory and executed on the processor, the computer instructions, when executed by the processor, performing the steps of the method of the first aspect.
A computer readable storage medium storing computer instructions which, when executed by a processor, perform the steps of the method of the first aspect.
The invention has the beneficial effects that:
1. the method can obtain the optimal sparse representation of the image to be recovered by adopting a multiple sparse representation method, can realize the high-precision reconstruction of the target image by combining a Bayesian compressed sensing method, and effectively improves the success rate of the reconstruction.
2. The method has no specific requirements on the adopted sparse transform method, overcomes the reversibility limitation of introducing sparse representation by a comprehensive method, allows the adoption of any number of sparse transforms, and can effectively improve the convergence rate of the algorithm in a combined sparse domain.
3. The method introduces CGM iterative computation image estimation mean value, and utilizes intermediate variables in the iterative process to estimate the hyperparameter and equality variance of Bayesian compressed sensing, thereby avoiding the computation of covariance matrix of large-scale images and effectively reducing memory requirement and computation amount.
4. The image recovery method based on the equality structure multiple regularization is suitable for recovering the image with high signal-to-noise ratio, and has higher reconstruction precision and higher convergence rate under the condition of high signal-to-noise ratio due to the equality structure.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description serve to explain the invention and not to limit the invention.
FIG. 1 is a diagram of a multi-regularized multi-level model of the present invention based on an equality structure;
FIG. 2 is an example of a segmented sparse signal;
FIG. 3 is a piecewise sparse signal recovery uncertainty performance curve;
FIG. 4 is a piecewise sparse signal recovery sparsity performance curve;
FIG. 5 is a plot of the signal-to-noise ratio performance of segmented sparse signal recovery;
fig. 6 is an original image for image restoration: a biological cell;
fig. 7 is an original image for image restoration: an electronic circuit diagram;
fig. 8 is an original image for image restoration: the moon;
fig. 9 is an original image for image restoration: automobile tires;
fig. 10(a) shows the result of recovery using E-MRSB biological cell image when SNR is 20 dB;
fig. 10(b) shows the result of image restoration using ADMM when SNR is 20 dB;
fig. 10(c) shows the result of restoring the biological cell image by the proximal method when the SNR is 20 dB;
fig. 11(a) shows the result of image restoration using an E-MRSB electronic circuit when the SNR is 20 dB;
fig. 11(b) shows the result of image restoration using the ADMM electronic circuit when the SNR is 20 dB;
fig. 11(c) shows the result of electronic circuit image restoration by the proximal method when the SNR is 20 dB;
fig. 12(a) shows the result of the recovery of the moon image using E-MRSB when the SNR is 20 dB;
fig. 12(b) shows the result of the ADMM lunar image restoration when the SNR is 20 dB;
fig. 12(c) shows the result of restoring the moon image by the proximal method when the SNR is 20 dB;
fig. 13(a) shows the result of the vehicle tire image recovery using E-MRSB when the SNR is 20 dB;
fig. 13(b) shows the result of the vehicle tyre image restoration using the ADMM when the SNR is 20 dB;
fig. 13(c) shows the result of recovering the automobile tire image by using proximal method when SNR is 20 dB;
fig. 14(a) shows the result of recovery using E-MRSB biological cell image when SNR is 40 dB;
fig. 14(b) shows the result of image restoration using ADMM when SNR is 40 dB;
fig. 14(c) shows the result of restoring the biological cell image by the proximal method when the SNR is 40 dB;
fig. 15(a) shows the result of image restoration using an E-MRSB electronic circuit when the SNR is 40 dB;
fig. 15(b) shows the result of image restoration using the ADMM electronic circuit when the SNR is 40 dB;
fig. 15(c) shows the result of restoring the electronic circuit image by the proximal method when the SNR is 40 dB;
fig. 16(a) shows the result of the recovery of the moon image using E-MRSB when the SNR is 40 dB;
fig. 16(b) shows the result of the ADMM lunar image restoration when the SNR is 40 dB;
fig. 16(c) shows the result of restoring the moon image by the proximal method when the SNR is 40 dB;
fig. 17(a) shows the result of the vehicle tire image restoration using E-MRSB when the SNR is 40 dB;
fig. 17(b) shows the result of the vehicle tire image restoration using the ADMM when the SNR is 40 dB;
fig. 17(c) shows the result of the automobile tire image restoration by the proximal method when the SNR is 40 dB.
Detailed Description
The invention is further described with reference to the following figures and examples.
It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
Example 1
As shown in fig. 1, in the image restoration method based on multiple regularization of an equation structure provided in this embodiment, a plurality of sparse transformations are introduced through the equation structure, that is, a plurality of independent Delta probability density functions are introduced, a multi-level bayesian model with multiple constraints is established through bayesian law, sparsity assumption is given to transformation coefficients corresponding to each transformation, so that a conjugate matching relationship between each hierarchy is established, and finally, fast reconstruction of a target image is achieved through iteration of an Expectation Maximization (EM) method in combination with a Conjugate Gradient Method (CGM).
The image restoration method based on the equation structure multiple regularization comprises the following steps:
step (1): on the premise of knowing a measurement matrix and an observation vector, establishing a linear equation for image recovery; that is, according to the linear relationship, the observation vector is equal to the product of the measurement matrix and the one-dimensional vectorization target image to be reconstructed, and a measurement likelihood function adopted in the bayesian inference, that is, formula (1), is constructed.
The method specifically comprises the following steps: assuming that the target image to be restored is represented as a two-dimensional matrix X, by concatenating all column vectors of X into one column vector X, assume that
Figure BDA0003097127870000071
An observation vector can be established
Figure BDA0003097127870000072
Linear relation to target signal x
y＝Ax+n (1)
Wherein the content of the first and second substances,
Figure BDA0003097127870000073
in order to measure the matrix of the measurements,
Figure BDA0003097127870000074
for a complex Gaussian white equation, M is typically satisfied<N。
Step (2): selecting a plurality of sparse transformations based on the constructed measurement likelihood function, and giving a plurality of probability density functions which are independent from each other on the basis of sparse transformation coefficients to calculate the conditional prior probability density of the target image;
selecting a reasonable sparse representation method according to prior information, and establishing a sparse representation coefficient equation; that is, according to the selected plurality of sparse transform methods, a plurality of independent Delta probability density functions are given based on the sparse representation coefficients to estimate the conditional prior probability density of the target image.
Specifically, the method comprises the following steps: selecting J complex-domain sparse transforms to DjIs shown in which
Figure BDA0003097127870000075
NjThe dimension of the sparse coefficient of the jth transform domain, J is 1,2, …, J, so the transform coefficient is expressed as
sj＝Djx (2)
Wherein
Figure BDA0003097127870000081
It can be seen that the introduced conditional prior probability density function of x is p(s)j|x)＝δ(sj-Djx), where δ represents a Delta function.
And (3): calculating a mean expression of the target image according to a Bayes rule based on the conditional prior probability density of the target image; and acquiring an image to be restored, and performing target image mean value estimation on the image to be restored based on the mean value expression of the target image.
Target image mean and covariance estimation is achieved through an EM algorithm in combination with CGM iteration; specifically, the method comprises the following steps:
step (3.1): according to Bayes calculation, adopting CGM iteration to calculate the mean value of the target image to be reconstructed, and extracting vector parameters in CGM iteration;
step (3.2): calculating an intermediate variable for subsequent parameter reconstruction according to the relation between the CGM vector parameter and the image covariance without completely recording an image covariance matrix;
the steps of step (3.1) and step (3.2) are:
obtaining conditional posterior probability density p (x | y; gamma) according to EM principleG,σ2) Satisfy normal distribution
Figure BDA0003097127870000082
I.e. p (x | y; Γ)G,σ2)＝CN(μx,Σx) Which isMean expression of target image
μx＝σ2∑xAHy (4)
Figure BDA0003097127870000083
Figure BDA0003097127870000084
Mean value μxI.e. the estimated mean, the subscript G denotes the sparse set of labels, i.e. G ═ {1,2, …, J }. Since in the subsequent steps the covariance matrix sigma is used several timesxTherefore, the matrix inversion in the direct calculation formula (5) is generally adopted, but for large-scale signals, such as 512 × 512 pixel images, the direct inversion is not only unacceptable in terms of calculation amount, but also can not be realized by a conventional computer memory. The invention adopts CGM method to iteratively calculate the mean value muxSum and covariance matrix ∑xThe relevant intermediate variables, the method is as follows:
introducing matrix
Figure BDA0003097127870000091
Equation (4) can be written as a linear hermitian equation
Lxμx＝σ2AHy (7)
According to the CGM principle, a formula linear Hermite equation is written into a linear equation form Bx ═ B, wherein B ═ Lx，x＝μx，b＝σ2AHy, then the solving step is
(a) Initialization: x is the number of(0)＝BHb，r(0)＝b-Bx(0)And w(0)＝r(0)；
(b) For the kth iteration, the following steps are completed:
Figure BDA0003097127870000092
x(k+1)＝x(k)+ζ(k)w(k)
r(k+1)＝r(k)-ζ(k)Bw(k)
Figure BDA0003097127870000093
w(k+1)＝r(k+1)+β(k)w(k)
wherein, the upper corner mark k represents the iteration times, and the column vector of each iteration forms a matrix Wk＝[Wk-1w(k)]Satisfy LxIn a conjugate relationship, i.e.
Figure BDA0003097127870000094
Thus covariance matrix
Figure BDA0003097127870000095
Can be expressed as
∑x＝∑kw(k)(w(k))H (8)
Then ΣxCan be represented as
diag(∑x)＝∑k|w(k)|2 (9)
Introducing auxiliary variables
Figure BDA0003097127870000101
To obtain
Figure BDA0003097127870000102
Finally, intermediate variables are calculated
Figure BDA0003097127870000103
Step (3.3): calculating a hyper-parameter and an equality variance by using the intermediate variable obtained by the calculation in the step (3.2); specifically, the method comprises the following steps:
assuming transform coefficients sjGaussian distribution, i.e. s, subject to independent equal distributionj～CN(0,Γj) Wherein the covariance matrix ΓjIs a diagonal matrix, and the diagonal elements are hyper-parameters gammaj. According to the M-step of the EM algorithm, calculating the hyper-parameter gammaj：
Figure BDA0003097127870000104
Wherein the content of the first and second substances,
Figure BDA0003097127870000105
the calculation is performed using equation (11) without calculating Σ by matrix inversionx. Similarly, calculate equation variance
Figure BDA0003097127870000106
Wherein the content of the first and second substances,
Figure BDA0003097127870000107
representing an equality variance estimation value obtained by the last iteration; tr (Sigma)x∑0) Is calculated as shown in equation (12), and thus the covariance matrix does not need to be calculated.
Step (3.4): judging iteration convergence, and if one of convergence conditions is met, ending iteration and outputting an estimation result of an image mean value; if not, continuing the iteration.
The convergence conditions include:
(1)
Figure BDA0003097127870000108
wherein tol is the tolerance;
(2)
Figure BDA0003097127870000109
the tolerance tol may be set to the same value as the condition (1), wherein
Figure BDA00030971278700001010
Figure BDA00030971278700001011
(3) Number of iterations k>Presetting maximum iteration frequency Imax。
The image restoration method based on the equality structure multiple regularization comprises the steps of receiving an image to be restored, converting the image into a one-dimensional signal, and projecting the one-dimensional signal to an observation vector y by using a measurement matrix A; inputting the measurement matrix and the observation vector into an image recovery model based on multiple regularization of an equality structure to obtain a target image mean value; the image recovery model based on the equation structure multiple regularization realizes target image mean optimization through iterative update of hyper-parameters and equation variances.
The specific steps of realizing target image mean value optimization by iterative update of hyper-parameters and equation variances based on the image recovery model with the equation structure multiple regularization comprise:
(1) inputting: obtaining a sparse transform DjObservation vector y and measurement matrix A;
(2) initialization: maximum number of iterations ImaxTolerance tol, over-parameter initial value γjSum equation variance σ2；
(3) Solving equation (7) by using a conjugate gradient method according to the measurement matrix A and the observation vector y to obtain a mean value and a covariance of the target image, and calculating an intermediate variable according to equations (11) and (12), specifically:
the mean and covariance of the target image x are expressed as
μx＝σ2∑xAHy
Figure BDA0003097127870000111
Figure BDA0003097127870000112
Introducing matrix
Figure BDA0003097127870000113
The mean expression of the target image x can be written as a linear hermite equation
Lxμx＝σ2AHy
Writing a formula linear hermite equation into a linear equation form Bx ═ B, where B ═ Lx，x＝μx，b＝σ2AHy, then the solving step is
(a) Initialization: x is the number of(0)＝BHb，r(0)＝b-Bx(0)And w(0)＝r(0)；
(b) For the kth iteration, the following steps are completed:
Figure BDA0003097127870000121
x(k+1)＝x(k)+ζ(k)w(k)
r(k+1)＝r(k)-ζ(k)Bw(k)
Figure BDA0003097127870000122
w(k+1)＝r(k+1)+β(k)w(k)
wherein, the upper corner mark k represents the iteration times, and the column vector of each iteration forms a matrix Wk＝[Wk-1w(k)]Satisfy LxIn a conjugate relationship, i.e.
Figure BDA0003097127870000123
Covariance matrix
Figure BDA0003097127870000124
Is shown as
∑x＝∑kw(k)(w(k))H
∑xIs represented by a diagonal element of
diag(∑x)＝∑k|w(k)|2
Introducing auxiliary variables
Figure BDA0003097127870000125
To obtain
Figure BDA0003097127870000126
Calculating intermediate variables
Figure BDA0003097127870000127
(4) Estimating a hyper-parameter vector and an equation variance according to formulas (13) and (14) by using the intermediate variable and the target image mean value obtained by calculation in the step (3), specifically:
Figure BDA0003097127870000128
Figure BDA0003097127870000131
(5) judging whether the convergence condition is met, if not, returning to the step (3) to continue iteration; and if so, ending the iteration and outputting the estimated mean value of the target image.
The multiple regularization multi-level model is shown in fig. 1, wherein a single-circle node represents a variable (or a hyper-parameter) to be calculated, and a double-circle node represents a measured or observed parameter. Given x, the posterior probability density of the measurement vector y is expressed as
Figure BDA0003097127870000132
Considering p(s)j| x) independence between probabilities, p(s)1,s2,…,sJ| x) can be expressed as
Figure BDA0003097127870000133
Where the subscript G denotes a sparse set of indices, i.e., G ═ 1,2, …, J, can be found
Figure BDA0003097127870000134
Where p (x) is the probability of no information, so that the conjugate relationship between adjacent layers can be preserved.
In experiments, the image restoration method based on equation structure multiple regularization according to the present invention is referred to as E-MRSB for short. The segmented sparse signal to be restored consists of three parts which respectively correspond to the sparsity of the identity transformation, the first-order TV and the Haar wavelet transformation, and one signal example is shown in figure 2. In particular, sparsity of the segmented sparse signal is defined as the sum of sparsity of all intrinsic sparse signals, denoted by K. The columns of the measurement matrix a follow a standard normal distribution, with the columns being normalized to a unit norm. Each experiment was repeated 200 times, and in the inequality experiment, the certainty was defined as M/N and the sparsity was defined as K/N. The success rate of signal recovery is defined as the Normalized Mean Square Error (NMSE) satisfying a predetermined criterion NMSE<10-3When the signal is considered to be successfully recovered. NMSE is also a measure of performance in an equality experiment, defined as
Figure BDA0003097127870000135
Wherein x isgenIs the original signal to be recovered and,
Figure BDA0003097127870000141
is the estimation result of the method recovery.
The methods employed for alignment included two multiple regularization CS methods: ADMM and proximal methods. As can be seen from the results of FIG. 3 and FIG. 4, the success rate of E-MRSBL is the highest in terms of uncertainty and sparsity, which is significantly better than that of ADMM and proximal methods. In the case of multi-constraint regularization, the NMSE for segmenting sparse signals using the proximal method is generally greater than 0.6, which is considered as a recovery failure in this experiment. In order to clearly show the recovery performance of the signal-to-noise ratio (SNR), the logarithmic form of NMSE (Log-NMSE) is used in fig. 5, and from the results, E-MRSBL seems to be less advantageous under the condition of medium signal-to-noise ratio, i.e. 20-35dB, and is significantly advantageous under the condition of low signal-to-noise ratio.
In order to verify the effectiveness of multiple regularization, the multiple regularization method is adopted to verify the recovery performance of image data, and the joint sparse representation of identity transformation, first-order TV and non-local TV is respectively adopted. As shown in fig. 6-9, four images were used as raw data, including biological cells, electronic circuit diagrams, moon and car tires. The size of the image is 256, 256. And 3 methods of E-MRSBL, ADMM and proximal are respectively adopted for image recovery. The measurement matrix A is generated by using a scrambling block Hadamard set, and the uncertainty ratio of measurement is 0.625. In the experiment, the image restoration performance was compared under the conditions of 20dB and 40dB of signal-to-noise ratio, respectively, and the restoration results are shown in fig. 10 to 17. The image recovery performance was quantitatively measured using NMSE and Structural Similarity (SSIM) indices and the results at 20dB and 40dB signal-to-noise ratios are summarized in tables 1 and 2, respectively. For each image, the best performing is highlighted in bold. From the recovery results, the ADMM results are too smooth and the equation has little effect on the ADMM between 20-40 dB of signal-to-noise ratio. In general, the E-MRSBL achieves the best performance at signal-to-noise ratios of 20dB and 40 dB.
TABLE 1 NMSE/SSIM estimation results at 20dB signal-to-noise ratio
Figure BDA0003097127870000142
Figure BDA0003097127870000151
TABLE 2 NMSE/SSIM estimation results at 40dB signal-to-noise ratio
Figure BDA0003097127870000152
According to the method, the optimal sparse representation of the image to be recovered can be obtained by adopting a multiple sparse representation method, the high-precision reconstruction of the target image can be realized by combining a Bayesian compressed sensing method, and the reconstruction power is effectively improved; the adopted sparse transformation method has no specific requirements, the reversibility limitation of introducing sparse representation by a comprehensive method is overcome, any number of sparse transformations are allowed to be adopted, and the convergence rate of the algorithm can be effectively improved in a combined sparse domain; and finally, CGM is introduced to calculate the image estimation mean value in an iterative manner, and the intermediate variable in the iterative process is used for estimating the hyperparameter and the equality variance of Bayesian compressed sensing, so that the covariance matrix of the large-scale image is avoided, and the memory requirement and the calculated amount are effectively reduced.
Example 2
The embodiment provides an image recovery system based on multiple regularization of an equation structure, which includes:
the image receiving module is used for receiving the image to be recovered, converting the image into a one-dimensional signal and projecting the one-dimensional signal to an observation vector by using a measurement matrix;
the image restoration module is used for inputting the measurement matrix and the observation vector into an image restoration model based on multiple regularization of an equation structure to obtain a target image mean value; the image restoration model calculates the mean value and the intermediate variable of the target image by adopting a conjugate gradient method according to the measurement matrix and the observation vector; updating the hyperparametric vector and the equality variance of Bayesian compressed sensing by using the intermediate variable and the target image mean value obtained by calculation; judging whether a convergence condition is met, and if so, outputting a target image mean value; and otherwise, returning to recalculate the mean value and the intermediate variable of the target image by using the updated hyper-parameter vector and equation variance.
Example 3
The present embodiment also provides an electronic device, which includes a memory, a processor, and computer instructions stored in the memory and executed on the processor, wherein the computer instructions, when executed by the processor, perform the steps of the method of embodiment 1.
Example 4
The present embodiment also provides a computer-readable storage medium for storing computer instructions, which when executed by a processor, perform the steps of the method of embodiment 1.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. The image restoration method based on the equation structure multiple regularization is characterized by comprising the following steps:
after receiving an image to be restored, converting the image into a one-dimensional signal, and projecting the one-dimensional signal to an observation vector by using a measurement matrix;
inputting the measurement matrix and the observation vector into an image recovery model based on multiple regularization of an equality structure to obtain a target image mean value; the image restoration model calculates the mean value and the intermediate variable of the target image by adopting a conjugate gradient method according to the measurement matrix and the observation vector; updating the hyperparametric vector and the equality variance of Bayesian compressed sensing by using the intermediate variable and the target image mean value obtained by calculation; judging whether a convergence condition is met, and if so, outputting a target image mean value; and otherwise, returning to recalculate the mean value and the intermediate variable of the target image by using the updated hyper-parameter vector and equation variance.
2. The image restoration method based on the equality structure multiple regularization as claimed in claim 1 wherein the conditional posterior probability density of the target image satisfies a normal distribution.
3. The image restoration method based on the equality structure multiple regularization as claimed in claim 2 wherein the intermediate variables are derived from the relationship between CGM vector parameters and image covariance.
4. The method for image restoration based on equation structure multiple regularization as claimed in claim 1 wherein the conditional prior probability density of the target image is obtained based on sparse representation coefficients in combination with a plurality of independent Delta probability density functions.
5. The method for image restoration based on equation structure multiple regularization as claimed in claim 1 wherein the observation vector is the product of a measurement matrix and a one-dimensional vectorized target image.
6. An image restoration system based on multiple regularization of an equation structure, comprising:
the image receiving module is used for receiving the image to be recovered, converting the image into a one-dimensional signal and projecting the one-dimensional signal to an observation vector by using a measurement matrix;
the image restoration module is used for inputting the measurement matrix and the observation vector into an image restoration model based on multiple regularization of an equation structure to obtain a target image mean value; the image restoration model calculates the mean value and the intermediate variable of the target image by adopting a conjugate gradient method according to the measurement matrix and the observation vector; updating the hyperparametric vector and the equality variance of Bayesian compressed sensing by using the intermediate variable and the target image mean value obtained by calculation; judging whether a convergence condition is met, and if so, outputting a target image mean value; and otherwise, returning to recalculate the mean value and the intermediate variable of the target image by using the updated hyper-parameter vector and equation variance.
7. The image restoration system based on the equality structure multiple regularization as claimed in claim 1 wherein the conditional posterior probability density of the target image satisfies a normal distribution.
8. The image restoration system based on the multiple regularizations of the equation structure as claimed in claim 1, wherein the conditional prior probability density of the target image is obtained based on sparse representation coefficients in combination with a plurality of Delta probability density functions that are independent of each other.
9. An electronic device comprising a memory and a processor and computer instructions stored on the memory and executable on the processor, the computer instructions when executed by the processor performing the steps of the method of any of claims 1 to 5.
10. A computer-readable storage medium storing computer instructions which, when executed by a processor, perform the steps of the method of any one of claims 1 to 5.
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