CN110728728A - Compressed sensing network image reconstruction method based on non-local regularization - Google Patents

Compressed sensing network image reconstruction method based on non-local regularization Download PDF

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CN110728728A
CN110728728A CN201910874274.6A CN201910874274A CN110728728A CN 110728728 A CN110728728 A CN 110728728A CN 201910874274 A CN201910874274 A CN 201910874274A CN 110728728 A CN110728728 A CN 110728728A
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孙玉宝
杨莹
陈基伟
刘青山
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Nanjing University of Information Science and Technology
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Abstract

The invention discloses a compressed sensing network image reconstruction method based on non-local regularization, which comprises the steps of firstly obtaining image data, carrying out normalization processing, sampling an image sequence and obtaining a corresponding measurement vector; acquiring the size of an image, setting random noise according to the size, constructing a compressed sensing network model, taking the random noise and a measurement vector as the input of a network, adding non-local regular constraint, designing a target function, and presetting the hyper-parameters of the network model; solving the designed objective function by adopting a semi-quadratic splitting algorithm, alternately and iteratively optimizing the constructed compressed sensing network model, and updating regular term parameters until an iteration ending condition is met; after the iteration process is finished, a reconstructed picture sequence is obtained through calculation according to the current iteration result, and therefore the compressed sensing network reconstruction with the non-local regular constraint is achieved. The invention can reconstruct the image close to the original image without pre-training the network under the condition of low sampling.

Description

Compressed sensing network image reconstruction method based on non-local regularization
Technical Field
The invention belongs to the technical field of image information processing, and particularly relates to an image reconstruction method based on a non-local regularization compressed sensing network.
Background
Compressed Sensing (CS) is a novel signal acquisition theory, combines traditional sampling and compression processes, can directly acquire measurement data far below the Nyquist sampling rate, can reduce sampling cost and storage resources, and meanwhile, the encoding end of the Compressed Sensing model only needs to perform linear random measurement, and the complex optimization process of reconstructing signals is completed at the decoding end.
The classic compressed sensing reconstruction algorithm depends on that an image has sparsity in a certain transform domain, and the image is reconstructed by solving a corresponding sparse coding problem, but the reconstruction quality is low under the condition of low sampling rate. At present, compressed sensing reconstruction algorithms based on deep learning are widely concerned due to high reconstruction quality, but the algorithms need to be pre-trained on a large number of data sets, and meanwhile, network models need to be retrained again aiming at different sampling rates and different measurement matrixes.
Aiming at the problems of the compression imaging system, the direct learning compression sensing network is an effective solution. Recently, Depth Image Priors (DIP) are an emerging model, i.e. without pre-training, the network itself has the capability to capture image priors. Therefore, DIP bridges the need for pre-trained deep learning methods and classical model-driven methods, and has been applied to many image anti-problems such as denoising, restoration, and super-resolution.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides a compressed sensing network image reconstruction method based on non-local regularization, which aims at the problems that the reconstruction quality of a classical algorithm is low under a low sampling rate and the conventional deep learning method needs a time-consuming pre-training process. According to the method, pre-training is not needed for the network, a non-local thought is introduced, and the pixel distribution of the reconstructed image is closer to the original image through mutual constraint of the data fidelity term and the non-local regular term, so that the accuracy of the reconstructed image under a low sampling rate is improved.
The technical scheme is as follows: in order to realize the purpose of the invention, the technical scheme adopted by the invention is as follows: a compressed sensing network image reconstruction method based on non-local regularization comprises the following steps:
s1, acquiring picture data, and carrying out normalization processing to obtain a picture sequence to be sampled; sampling the image sequence to obtain a corresponding measurement vector;
s2, obtaining the size of the picture to be reconstructed, and setting random noise according to the size; constructing a compressed sensing network model, taking random noise and the measurement vector obtained in the step S1 as the input of the network, adding a non-local regular constraint, designing a target function of the non-local regular compressed sensing network model, and presetting the hyper-parameters of the network model;
s3, solving the objective function in the step S2 by adopting a half-quadratic splitting algorithm, alternately and iteratively optimizing the constructed compressed sensing network model, and updating regular term parameters until an iteration ending condition is met;
and S4, after the iteration process is finished, calculating to obtain a reconstructed picture sequence according to the current iteration result, thereby realizing the picture reconstruction of the compressed sensing network with the non-local regular constraint.
Further, the acquiring of the image data in step S1, after normalization processing, performing random gaussian sampling on the image to obtain a corresponding measurement vector, specifically includes:
y＝Φx y∈RM，Φ∈RM×N，x∈RN
wherein y represents a measurement vector, phi represents a Gaussian random measurement matrix, x represents an image after normalization processing, M represents the size of the measurement vector, and N is the pixel number of the image.
Further, in step S2, acquiring a size of the picture to be reconstructed, and setting a random noise according to the size; constructing a compressed sensing network model, taking random noise and the measurement vector obtained in the step S1 as the input of the network, adding a non-local regular constraint, designing a target function of the non-local regular compressed sensing network model, and presetting the hyper-parameters of the network model; the method specifically comprises the following steps:
the objective function of the compressed sensing network model added with the non-local regular constraint is as follows:
Figure BDA0002203831840000021
wherein the first term is a data fidelity term, the second term is a non-local regularization term, λ is a regularization parameter that balances the two terms, uw(z)∈RH×W×CIs the input of the network model, H, W and C represent the length, width and number of channels of the image, respectively, z represents the randomly generated noise, W represents the parameters of the network model, yi∈RMIs a measurement vector, P, corresponding to the ith frame of the image sequenceiIs an extraction function for extracting uwFrame i of (z) and converted to vector form H × W, Φ being a gaussian random measurement matrix.
And solving the reconstructed image by minimizing the objective function and utilizing the constructed network model.
Presetting the hyper-parameters of the network model comprises the following steps: setting the learning rate of the network to be 0.01 and the non-local regularization initial parameter to be 0; and setting the iteration times T of the optimized network model.
Further, the iteration ending condition in step S3 means that a preset iteration number T is reached, or the iteration process converges.
Further, in step S3, a half-quadratic splitting algorithm is used to solve an objective function of the non-local regular compressed sensing network model, the constructed compressed sensing network model is alternately optimized in an iterative manner, and regular term parameters are updated until an iteration end condition is satisfied; the method comprises the following specific steps:
s31, introducing an auxiliary variable g to change the objective function of the network model into
Figure BDA0002203831840000022
S32, changing the formula (2) into an unconstrained optimization problem by using a Lagrange multiplier method, namely:
Figure BDA0002203831840000031
wherein gamma is uwPenalty parameter between (z) and gCounting;
s33, fixing the auxiliary variable g according to the formula (3), namely updating the network model parameter w through solving the formula (4) on the basis of the invariance of g;
Figure BDA0002203831840000032
updating and generating network parameter w by solving formula (4) by adopting Adam algorithmk+1：
Figure BDA0002203831840000033
wk+1←wk-αAdam(wk，dw) (6)
Where α is the learning rate of the network model, set to 0.01; dw represents the gradient of w; k represents the current iteration number;
s34, according to the formula (3), fixing the network parameter w, namely updating the auxiliary variable g by solving the formula (7) on the basis of keeping w unchanged, and updating the penalty parameter gamma,
s35, updating the current iteration number to be k +1, if k +1 is less than T, calculating and judging whether the current iteration is converged, and entering the step S36; if k +1 is larger than or equal to T, calculating according to the current iteration result to obtain a reconstructed picture sequence;
s36, if the current iteration is not converged, alternately iterating to execute steps S33-S35; if the current iteration converges, the process proceeds to step S4.
Further, the step S35 calculates and determines whether the current iteration converges, specifically:
the convergence criterion RelErr at the k +1 th iteration is calculated as follows:
Figure BDA0002203831840000035
setting a first threshold value epsilon1When Rel isErr＜ε1And judging that the current iteration converges, otherwise, judging that the current iteration does not converge.
Further, in step S4, after the iteration process is finished, a reconstructed picture sequence is calculated according to the current iteration result; the method specifically comprises the following steps:
if the (k + 1) th iteration converges, outputting the updated (k + 1) th iteration
Figure BDA0002203831840000036
And
Figure BDA0002203831840000037
final output result of network model
Figure BDA0002203831840000038
The corresponding reconstructed picture.
Has the advantages that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
the invention utilizes the compression perception theory to establish an image reconstruction method based on a non-local regular compression perception network, the model can preliminarily reconstruct the original image without pre-training under the condition of low sampling rate of an image sequence, meanwhile, the non-local regular constraint is utilized to further consider the global information of the image sequence and enhance the robustness of image noise, so that the pixel distribution of the reconstructed image is closer to the original image, and the aim of accurately reconstructing the original image under the condition of low sampling rate is fulfilled.
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FIG. 1 is a schematic flow diagram of an embodiment of the method of the present invention;
FIG. 2 is a detailed block diagram of a compressed sensing network constructed by the present invention;
FIG. 3 is a block diagram of a compressive sensing network model constructed in accordance with the present invention;
FIG. 4 is a schematic view of the present invention using a semi-quadratic splitting algorithm for alternate optimization;
FIG. 5 is the comparison of the reconstructed image of the butterfly picture in the Set5 data with the real image for each algorithm;
FIG. 6 is a comparison of reconstructed images of penguin pictures in the BSD68 dataset with real images for each algorithm;
FIG. 7 is a comparison of the reconstructed image of the STARE data set with a real image for each algorithm;
fig. 8 is the comparison result of the algorithms for the reconstructed image and the real image of the Foreman video sequence;
fig. 9 is a graph of peak signal-to-noise ratio of the reconstruction result of the algorithm of the present invention at Set5 and the video sequence Foreman under different noise intensity interferences.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention relates to a compressed sensing network image reconstruction method based on non-local regularization, which has a specific flow shown in figure 1 and comprises the following steps:
s1, acquiring picture data, and carrying out normalization processing to obtain a picture sequence to be sampled; sampling the image sequence to obtain a corresponding measurement vector; the method specifically comprises the following steps:
y＝Φx y∈RM，Φ∈RM×N，x∈RN
wherein y represents a measurement vector, phi represents a Gaussian random measurement matrix, x represents an image after normalization processing, M represents the size of the measurement vector, and N is the pixel number of the image.
S2, obtaining the size of the picture to be reconstructed, and setting random noise according to the size; constructing a compressed sensing network model, wherein the structure of the network model is shown in FIG. 3; taking the random noise and the measurement vector obtained in the step S1 as the input of the network, adding a non-local regular constraint, designing a target function of a non-local regular compressed sensing network model, and presetting the hyper-parameters of the network model; the method comprises the following specific steps:
the objective function of the compressed sensing network model added with the non-local regular constraint is as follows:
Figure BDA0002203831840000051
wherein the first term is a data fidelity term, the second term is a non-local regularization term, λ is a regularization parameter that balances the two terms, uw(z)∈RH×W×CIs the input of the network model, H, W and C represent the length, width and number of channels of the image, respectively, z represents the randomly generated noise, W represents the parameters of the network model, yi∈RMIs a measurement vector, P, corresponding to the ith frame of the image sequenceiIs an extraction function for extracting uwFrame i of (z) and converted to vector form H × W, Φ being a gaussian random measurement matrix.
And solving the reconstructed image by minimizing the objective function and utilizing the constructed network model.
Presetting the hyper-parameters of the network model comprises the following steps: setting the learning rate of the network to be 0.01 and the non-local regularization initial parameter to be 0; and setting the iteration times T of the optimized network model.
S3, solving the objective function in the step S2 by adopting a half-quadratic splitting algorithm, alternately and iteratively optimizing the constructed compressed sensing network model, and updating regular term parameters until an iteration ending condition is met; the iteration ending condition refers to that a preset iteration time T is reached or an iteration process is converged; the network model is alternately optimized by using a semi-quadratic splitting algorithm as shown in FIG. 4; the method comprises the following specific steps:
s31, introducing an auxiliary variable g to change the objective function of the network model into
S32, changing the formula (2) into an unconstrained optimization problem by using a Lagrange multiplier method, namely:
Figure BDA0002203831840000053
wherein gamma is uwA penalty parameter between (z) and g;
s33, fixing the auxiliary variable g according to the formula (3), namely updating the network model parameter w through solving the formula (4) on the basis of the invariance of g;
Figure BDA0002203831840000054
updating and generating network parameter w by solving formula (4) by adopting Adam algorithmk+1：
Figure BDA0002203831840000055
wk+1←wk-αAdam(wk，dw) (6)
Where α is the learning rate of the network model, set to 0.01; dw represents the gradient of w; k represents the current iteration number;
s34, according to the formula (3), fixing the network parameter w, namely updating the auxiliary variable g by solving the formula (7) on the basis of keeping w unchanged, and updating the penalty parameter gamma,
s35, updating the current iteration number to be k +1, if k +1 is less than T, calculating and judging whether the current iteration is converged, and entering the step S36; if k +1 is larger than or equal to T, calculating according to the current iteration result to obtain a reconstructed picture sequence;
calculating and judging whether the current iteration is converged, specifically comprising the following steps:
the convergence criterion RelErr at the k +1 th iteration is calculated as follows:
Figure BDA0002203831840000062
setting a first threshold value epsilon1When RelErr < ε1Judging that the current iteration converges, otherwise, judging that the current iteration converges;
s36, if the current iteration is not converged, alternately iterating to execute steps S33-S35; if the current iteration converges, the process proceeds to step S4.
And S4, after the iteration process is finished, calculating to obtain a reconstructed picture sequence according to the current iteration result, thereby realizing the picture reconstruction of the compressed sensing network with the non-local regular constraint. The method specifically comprises the following steps:
if the (k + 1) th iteration converges, outputting the updated (k + 1) th iteration
Figure BDA0002203831840000063
Yang gk+1Final output of the network modelThe corresponding reconstructed picture.
In order to verify the effect of the invention, the invention is subjected to a simulation experiment, tests are carried out on different data sets Set5, BSD68, STARE and Foreman video sequences, and relevant parameters are Set: the learning rate α is 0.01, and the number of iterations is 2000. All parameters of the network are initialized randomly since the network does not need to be pre-trained.
The evaluation of the experiment used both qualitative and quantitative analytical methods.
FIG. 5 shows the present invention and TVAL3, BCS-SPL-DCT, Reconnet, ISTA-Net2Comparing the image reconstruction effects of the four algorithms at the sampling rates of 0.04 and 0.1 respectively; the sampling rate is 0.04 in fig. 5(a) and 0.1 in fig. 5 (b). As can be seen from FIG. 5, the reconstruction effect of the present invention is significantly better than that of TVAL3, BCS-SPL-DCT, Reconnet, ISTA-Net2These four algorithms.
For quantitative analysis comparison, MSE, PSNR and SSIM are used to evaluate image quality, and reconstruction time (time unit is millisecond) of a single image is used to evaluate reconstruction speed of the algorithm. Where MSE is Mean square error (Mean squared error), i.e. average error of a single pixel in an image, PSNR is Peak Signal to Noise Ratio (Peak Signal to Noise Ratio), SSIM is structural similarity index (structural similarity index), and the calculation is as follows:
Figure BDA0002203831840000071
Figure BDA0002203831840000072
Figure BDA0002203831840000073
wherein,
Figure BDA0002203831840000074
is the reconstructed image, and x(i)Is the original image, i.e. the real image. s is the total number of pixels of the image, range represents the dynamic range of image pixel values,
Figure BDA0002203831840000075
is an image
Figure BDA0002203831840000076
Pixel mean of (d), muxIs the pixel mean, σ, of the image xxIs the variance of the x pixels of the image,
Figure BDA0002203831840000078
is image x and image
Figure BDA0002203831840000077
Covariance of c1＝(k1L)2，c2＝(k2L)2Is a constant for maintaining stability, L is the dynamic range of pixel values, k1＝0.01，k2＝0.03。
When making quantitative comparison, selecting test picture from different data sets, after reading the size of said picture, according to said size producing correspondent test pictureThe random noise is input into a compressed sensing network model designed by the method, a reconstructed image is calculated and output through the model, the reconstructed image is compared with an original image, and corresponding MSE, PSNR and SSIM values are calculated. FIG. 5 shows the algorithm of the present invention and TVAL3, BCS-SPL-DCT, Reconnet, ISTA-Net under the Set5 data Set+PSNR values of the four algorithms under the conditions that the sampling rates are 0.04 and 0.1 are higher, and the higher the PSNR value is, the better the image quality is; the sampling rate is 0.04 in fig. 5(a) and 0.1 in fig. 5 (b).
FIG. 6 shows the algorithm of the present invention and TVAL3, Reconnet, ISTA-Net+The three algorithms respectively have PSNR values at BSD68 data set with a sampling rate of 0.04. By comparison, it is evident that the method of the present invention has better reconstruction quality and does not appear to ReconNet and ISTA-Net at low sampling rates+The same blocking effect.
FIG. 7 shows a comparison of PSNR results for a complex color image on a STARE data set at a sample rate of 0.04 for the method of the present invention and CS-DIP. Compared with the CS-DIP, the method can reconstruct more texture details and has better reconstruction quality.
Fig. 8 shows the comparison between the method of the present invention and the two algorithms MC-BCS-SPL and ISTA-Net + under the condition that the sampling rate is 0.04 on the video data set Foreman. Through the visual contrast chart, the method can achieve a good reconstruction result aiming at the video.
Meanwhile, in order to further verify the robustness of the method to noise, the method provided by the invention with the non-local regular constraint is abbreviated as NLR-CSNet, and the method without the non-local regular constraint is abbreviated as Plain-CSNet. Four levels (0.01, 0.04, 0.1, 0.25) of gaussian noise are added to the measurement matrix y, and fig. 9(a) illustrates PSNR curves of the two algorithms at different sampling rates on the picture data Set 5. Fig. 9(b) illustrates PSNR curves for two algorithms at different sampling rates on a video data set. According to the two graphs, it can be clearly seen that the method provided by the invention with the non-local regular constraint is more robust to noise.
In summary, compared with the conventional compressed sensing, the reconstruction iteration time is long, the reconstruction quality is poor under a low sampling rate, and the current deep learning needs to be pre-trained on a large number of data sets and needs to be retrained for a new sampling rate and a measurement matrix. The invention utilizes the idea that the depth network which is not pre-trained can fully capture image prior to establish an image reconstruction model of the network based on the non-local regular compressed sensing, and utilizes the network prior and the additional non-local regular prior to fully consider the local and non-local information of the image, so that the reconstruction of the complex image under the low sampling rate has better effect. The invention can reconstruct the gray natural image, and can also reconstruct the continuous video frame and the complex color image. Meanwhile, under the interference of a certain noise degree, the method has better robustness. Compared with a classical model-driven algorithm and a depth-based compressed sensing algorithm, the method has certain advantages.

Claims (8)

1. A compressed sensing network image reconstruction method based on non-local regularization is characterized in that: the method comprises the following steps:
s1, acquiring picture data, and carrying out normalization processing to obtain a picture sequence to be sampled; sampling the image sequence to obtain a corresponding measurement vector;
s2, obtaining the size of the picture to be reconstructed, and setting random noise according to the size; constructing a compressed sensing network model, taking random noise and the measurement vector obtained in the step S1 as the input of the network, adding a non-local regular constraint, designing a target function of the non-local regular compressed sensing network model, and presetting the hyper-parameters of the network model;
s3, solving the objective function in the step S2 by adopting a half-quadratic splitting algorithm, alternately and iteratively optimizing the constructed compressed sensing network model, and updating regular term parameters until an iteration ending condition is met;
and S4, after the iteration process is finished, calculating to obtain a reconstructed picture sequence according to the current iteration result, thereby realizing the picture reconstruction of the compressed sensing network with the non-local regular constraint.
2. The method for reconstructing the compressed sensing network image based on the non-local regularization as claimed in claim 1, wherein: the step S1 is to acquire image data, perform normalization processing, and perform random gaussian sampling on the image to obtain a corresponding measurement vector, which specifically includes:
y＝Φx y∈RM,Φ∈RM×N,x∈RN
wherein y represents a measurement vector, phi represents a Gaussian random measurement matrix, x represents an image after normalization processing, M represents the size of the measurement vector, and N is the pixel number of the image.
3. The method for reconstructing a compressed sensing network image based on non-local regularization according to claim 2, wherein: step S2, constructing a compressive sensing network model, taking random noise and the measurement vector obtained in step S1 as the input of the network, adding a non-local regular constraint, and designing a target function of the non-local regular compressive sensing network model; the method comprises the following specific steps:
the objective function of the compressed sensing network model added with the non-local regular constraint is as follows:
wherein the first term is a data fidelity term, the second term is a non-local regularization term, λ is a regularization parameter that balances the two terms, uw(z)∈RH×W×CIs the input of the network model, H, W and C represent the length, width and number of channels of the image, respectively, z represents the randomly generated noise, W represents the parameters of the network model, yi∈RMIs a measurement vector, P, corresponding to the ith frame of the image sequenceiIs an extraction function for extracting uw(z) frame i and converted to vector form H × W, Φ is gaussian random measurement matrix;
and solving the reconstructed image by minimizing the objective function and utilizing the constructed network model.
4. The method according to claim 3, wherein the compressed sensing network image reconstruction method based on the non-local regularization is characterized in that: presetting the hyper-parameters of the network model comprises the following steps: setting the learning rate of the network to be 0.01 and the non-local regularization initial parameter to be 0; and setting the iteration times T of the optimized network model.
5. The method for reconstructing a compressed sensing network image based on non-local regularization according to claim 4, wherein: the iteration ending condition in step S3 is that a preset iteration number T is reached, or the iteration process converges.
6. The compressed sensing network image reconstruction method based on the non-local regularization according to any one of claims 3 to 5, characterized in that: in the step S3, a semi-quadratic splitting algorithm is used to solve an objective function of the non-local regular compressed sensing network model, the constructed compressed sensing network model is alternately and iteratively optimized, and regular term parameters are updated until an iteration end condition is satisfied; the method comprises the following specific steps:
s31, introducing an auxiliary variable g to change the objective function of the network model into
S32, changing the formula (2) into an unconstrained optimization problem by using a Lagrange multiplier method, namely:
wherein gamma is uwA penalty parameter between (z) and g;
s33, fixing the auxiliary variable g according to the formula (3), namely updating the network model parameter w through solving the formula (4) on the basis of the invariance of g;
Figure FDA0002203831830000023
updating and generating network parameter w by solving formula (4) by adopting Adam algorithmk+1：
Figure FDA0002203831830000024
wk+1←wk-αAdam(wk,dw) (6)
Wherein alpha is the learning rate of the network model, dw represents the gradient of w, and k represents the current iteration number;
s34, according to the formula (3), fixing the network parameter w, namely updating the auxiliary variable g by solving the formula (7) on the basis of keeping w unchanged, and updating the penalty parameter gamma,
Figure FDA0002203831830000025
s35, updating the current iteration number to be k +1, if k +1 is less than T, calculating and judging whether the current iteration is converged, and entering the step S36; if k +1 is larger than or equal to T, calculating according to the current iteration result to obtain a reconstructed picture sequence;
s36, if the current iteration is not converged, alternately iterating to execute steps S33-S35; if the current iteration converges, the process proceeds to step S4.
7. The method according to claim 6, wherein the compressed sensing network image reconstruction method based on the non-local regularization is characterized in that: in step S35, calculating and determining whether the current iteration converges, specifically:
the convergence criterion RelErr at the k +1 th iteration is calculated as follows:
setting a first threshold value epsilon1When RelErr < ε1Judging the current iteration receivingConvergence, otherwise, it is determined not to converge.
8. The method according to claim 7, wherein the compressed sensing network image reconstruction method based on the non-local regularization is characterized in that: in the step S4, after the iteration process is finished, a reconstructed picture sequence is calculated according to the current iteration result; the method specifically comprises the following steps:
if the (k + 1) th iteration converges, outputting the updated (k + 1) th iteration
Figure FDA0002203831830000032
And gk+1Final output of the network modelThe corresponding reconstructed picture.
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