A compressed sensing image reconstruction method, device, electronic device and storage medium

Abstract

The present invention discloses a method, device, electronic device and storage medium for compressed sensing image reconstruction, the method comprising: obtaining a cartoon texture decomposition model of an image to be reconstructed, the cartoon texture decomposition model comprising a cartoon part and a texture part; the cartoon part is modeled by adopting an isotropic total variation image restoration definition method; the texture part is modeled by adopting a convolution dictionary learning model based on non-convex optimization; an auxiliary parameter is introduced to expand the regularization term of the cartoon part by adopting isotropic total variation norm prior knowledge to obtain an optimization model; the sparse coefficient and texture dictionary of the texture part in the optimization model are updated respectively, and the smoothness parameter and auxiliary parameter of the cartoon part in the optimization model are updated respectively; and a reconstructed image is determined according to the updated cartoon part and texture part. The present invention can effectively accurately reconstruct different components of the image to be reconstructed, and finally obtain a reconstructed image of higher quality.

Description

Technical Field

[0001] The present invention relates to the field of image processing technology, and in particular to a compressed sensing image reconstruction method, device, electronic equipment and storage medium. Background Art

[0002] Compressed sensing (CS) uses a specific measurement matrix to map sparse signals in a certain transform domain from the original high-dimensional space to a low-dimensional space, obtain less measurement data, and solve the underdetermined ill-conditioned problem from low dimension to high dimension by solving a constrained optimization model to obtain a reconstructed image. Since CS realizes the sampling and compression of signals at the same time, it has the advantages of low sampling rate and high acquisition efficiency. It has received high attention and application in the fields of medical imaging, wireless communication, radar detection, etc., especially magnetic resonance image reconstruction based on CS has important research and clinical significance.

[0003] When solving the image inverse problem based on compressed sensing, the sparse representation model based on the L-norm can obtain more sparse representation coefficients, which helps to reconstruct higher quality images from undersampled measurement data.

[0004] However, image sparse representation models usually only have good sparse representation capabilities for certain specific structural features of the image. Since natural images have rich structural features, it is difficult to obtain the optimal sparse prior information when processing natural images using a single sparse representation model, which affects the quality of natural image reconstruction.

[0005] In addition, in order to reduce the small high-frequency oscillation artifacts in the CS reconstruction based on wavelet transform, a total variation penalty for the entire original image can be introduced. However, this easily leads to the loss of texture details in the image and tends to produce an overly smooth reconstruction effect. Summary of the invention

[0006] In view of this, the present invention provides a compressed sensing image reconstruction method, device, electronic device and storage medium to effectively reconstruct different components of the image to be reconstructed more accurately and obtain a reconstructed image with higher quality.

[0007] To this end, the present invention provides the following technical solutions:

[0008] In one aspect, the present invention provides a compressed sensing image reconstruction method, the method comprising:

[0009] Obtaining a cartoon texture decomposition model of the image to be reconstructed, the cartoon texture decomposition model comprising a cartoon part and a texture part; the cartoon part is modeled using an isotropic total variation image restoration definition method; the texture part is modeled using a convolutional dictionary learning model based on non-convex optimization;

[0010] Auxiliary parameters are introduced to expand the regularization term of the cartoon part using isotropic total variation norm prior knowledge to obtain an optimization model;

[0011] Respectively updating the sparse coefficients and texture dictionary of the texture part in the optimization model, and respectively updating the smooth parameters and auxiliary parameters of the cartoon part in the optimization model;

[0012] According to the updated cartoon section and texture section, use Determine the reconstructed image, where x is the reconstructed image, Indicates that D L α i Place it at the i-th position and fill the rest with zeros; D L is the updated texture dictionary, α i is the updated sparse, x C For the updated cartoon part.

[0013] Furthermore, the cartoon texture decomposition model is:

[0014]

[0015] Among them, Φ∈R M×N represents the measurement matrix, Represents the texture part of the image to be reconstructed, D L ∈R n×m Represents the texture dictionary, {α i}∈R m represents the corresponding sparse coefficient, Indicates that D L α i Place it at the i-th position and fill the rest with zeros; x C ∈R N Represents the cartoon part of the image to be reconstructed, which is modeled using the isotropic total variation image restoration definition method, with ||x C || TV Indicates; λ1, λ2, λ3 represent regularization coefficients; b is the initial input data, Ω1(x)=||x||0, indicating a zero sparsity constraint; Ω2 is in the form of an indicator function, expressed as: Among them, the set C is a unit norm ball used to limit the length of dictionary elements, which means that for D L Any column D L [:,j] satisfies

[0016] Furthermore, the optimization function is:

[0017] Among them, d υ and dh is an auxiliary variable; d υ =D v x C , d h =D h x C .

[0018] Further, updating the sparse coefficient of the texture part in the optimization model includes:

[0019] The update of sparse coefficients is regarded as a convolutional basis pursuit denoising problem;

[0020] The proximal gradient descent algorithm is used to solve the convolutional basis pursuit denoising problem and obtain the updated sparse coefficients:

[0021] Among them, η1 is the step size,

[0022] Further, updating the texture dictionary of the texture part in the optimization model includes:

[0023] Update the texture dictionary to:

[0024] in, Solve according to Kronecker's property.

[0025] Further, updating the smoothing parameters of the cartoon part in the optimization model includes:

[0026] The smoothing parameter x C The update of is considered as an optimization problem:

[0027]

[0028] in, d υ and d h is an auxiliary variable; μ represents the relaxation parameter; B is a convex set; λ 3,max yes The maximum eigenvalue of

[0029] The generalized accelerated proximal gradient method is used to solve the optimization problem and obtain the updated smoothing parameter x C :

[0030]

[0031]

[0032] Among them, the acceleration strategies of the generalized accelerated proximal gradient method include:

[0033] definition and as follows:

[0034]

[0035]

[0036] in, is a continuously differentiable function; prox is the proximal function.

[0037] Further, the auxiliary parameter d of the cartoon part in the optimization model is updated υ , d h ,include:

[0038] Update auxiliary variable d υ and d h for:

[0039]

[0040]

[0041] Among them, prox is the proximal function.

[0042] In another aspect, the present invention further provides a compressed sensing image reconstruction device, the device comprising:

[0043] An acquisition unit is used to acquire a cartoon texture decomposition model of an image to be reconstructed, wherein the cartoon texture decomposition model includes a cartoon part and a texture part; the cartoon part is modeled by using an isotropic total variation image restoration definition method; and the texture part is modeled by using a convolution dictionary learning model based on non-convex optimization;

[0044] An optimization unit is used to introduce auxiliary parameters to expand the regularization term of the cartoon part using isotropic total variation norm prior knowledge to obtain an optimization model;

[0045] An updating unit, used to update the sparse coefficients and texture dictionary of the texture part in the optimization model, and to update the smoothing parameters and auxiliary parameters of the cartoon part in the optimization model;

[0046] The determination unit is used to determine the reconstructed image according to the updated cartoon part and texture part.

[0047] On the other hand, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned compressed sensing image reconstruction method when executing the program.

[0048] On the other hand, the present invention further provides a computer-readable storage medium, in which a computer instruction set is stored. When the computer instruction set is executed by a processor, the compressed sensing image reconstruction method as described above is implemented.

[0049] Advantages and positive effects of the present invention: The compressed sensing image reconstruction method provided by the present invention, with the help of the cartoon texture decomposition model, proposes to use the isotropic total variation image restoration definition to reconstruct the cartoon part of the natural image, and uses a convolutional dictionary learning model based on non-convex optimization to reconstruct the texture part of the natural image, overcoming the defects of using the CSC model to represent the entire natural image. Experimental results show that the designed model can effectively reconstruct the different components of the natural image more accurately and obtain a higher quality reconstructed image. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0051] Figure 1 A schematic diagram of a flow chart of a compressed sensing image reconstruction method provided by an embodiment of the present invention;

[0052] Figure 2 A schematic diagram of the structure of a compressed sensing image reconstruction device provided by an embodiment of the present invention;

[0053] Figure 3 A schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0054] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0055] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0056] The present invention utilizes the image decomposition theory to decompose the natural image into a cartoon part and a texture part, integrates the sparse representation model based on the L norm and the total variation into the image cartoon-texture decomposition model, and uses the isotropic total variation image restoration definition and the L norm sparse representation model based on the cartoon-texture image separation model to perform optimal sparse representation on the cartoon component and the texture component of the natural image; the total variation method can obtain a more accurate gradient sparsity prior of the cartoon component of the image, so the isotropic total variation image restoration definition method is used to perform global sparse representation on the cartoon component. The convolutional sparse coding model has a good sparse representation capability for the texture part of the image, so the non-convex optimized convolution dictionary learning model based on the L norm is used to reconstruct the texture part of the natural image and obtain a sparser representation coefficient. Thereby, the optimal sparse prior information is obtained, and the quality of natural image reconstruction is improved.

[0057] like Figure 1 As shown, it shows a schematic flow chart of a compressed sensing image reconstruction method provided by an embodiment of the present invention, the method comprising:

[0058] S110 , obtaining a cartoon texture decomposition model of the image to be reconstructed, where the cartoon texture decomposition model includes a cartoon part and a texture part.

[0059] The natural image to be reconstructed generally includes a cartoon part and a texture part. The cartoon part and the texture part have different characteristics and contain different image information. The cartoon part reflects the smoothness of a large piece, while the texture part is generally very rough and has a strong image gradient. In the subsequent image reconstruction, different reconstruction methods can be used according to the different characteristics of the cartoon part and the texture part to obtain better image reconstruction effects.

[0060] Specifically, the cartoon texture decomposition model of the image to be reconstructed is described as follows:

[0061]

[0062] Among them, Φ∈RM×N represents the measurement matrix, Represents the texture part of the image to be reconstructed, D L ∈R n×m Represents the texture dictionary, {α i}∈R m represents the corresponding sparse coefficient, Indicates that D L α i Place it at the i-th position and fill the rest with zeros; x C ∈R N Represents the cartoon part of the image to be reconstructed, which is modeled using the isotropic total variation image restoration definition method, with ||x C || TV Indicates; λ1, λ2, λ3 represent regularization coefficients; b is the initial input data, Ω1(x)=||x||0, indicating a zero sparsity constraint; Ω2 is in the form of an indicator function, expressed as: Among them, the set C is a unit norm ball used to limit the length of dictionary elements, which means that for D L Any column D L [:,j] satisfies

[0063] S120. Expand the regularization term of the cartoon part using the isotropic total variation norm prior knowledge to obtain an optimized model.

[0064] In order to minimize the total variation norm of the smooth part in equation (1), the cartoon part of the cartoon texture separation model is modeled using the isotropic total variation image restoration definition method.

[0065] In one embodiment, the cartoon part of the cartoon texture decomposition model is represented as an isotropic total variation image restoration form to obtain an optimized model, including:

[0066] For the cartoon part of the cartoon texture separation model, the isotropic total variation image restoration definition method is used to model it, and the following is obtained:

[0067]

[0068] The above formula is equivalent to:

[0069] TV iso (x C )=||D υ (x C )D h (x C )|| iT ;

[0070] in:

[0071] p=Dv (x c ):R m×n →R (m-1)×n , p i,j =x i+1,j -x i,j ,i=1,…,m-1,j=1,…,n,

[0072] q=D h (x c ):R m×n →R m×(n-1) ,q i,j =x i,j+1 -x i,j ,i=1,…,m,j=1,…,n-1.

[0073] Introduce two auxiliary variables d v and d h , let d υ =p,d h =q, and the optimization model is obtained:

[0074]

[0075] where d υ =D υ x C , d h =D h x C .

[0076] In order to solve the optimization problem in equation (2), it is necessary to update the variables {α i}, D L , x C , d v , d h .

[0077] S130, respectively updating the texture part and the cartoon part in the optimization model to obtain an updated texture part and an updated cartoon part.

[0078] In order to facilitate the subsequent solution, let:

[0079]

[0080] In one embodiment, the sparse coefficients {α i},include:

[0081] {α i The update of} can be viewed as the following convolutional basis pursuit denoising problem:

[0082]

[0083] The proximal gradient algorithm is used to calculate the sparse coefficients {α i} is updated, and the updated sparse coefficient is:

[0084]

[0085] Among them, η1 is the step size.

[0086] In one embodiment, the dictionary D of the texture part in the optimization model is updated. L , updated as follows:

[0087]

[0088] According to Kronecker's product property, we can solve:

[0089]

[0090] In one embodiment, the cartoon part x in the optimization model is updated. C , as the following optimization problem:

[0091]

[0092] Further relaxing the equality constraints of the above formula yields:

[0093]

[0094] in, B is a convex set and μ represents the relaxation parameter.

[0095] definition and as follows:

[0096]

[0097]

[0098] in, is a continuously differentiable function that satisfies the following descent theorem:

[0099]

[0100] This definition applies to the generalized accelerated proximal gradient method used in this method. f Represents the Lipschitz constant. According to the definition of the Lipschitz constant, we can get L f =H(f), H(f) is the Hessian matrix of the function, and the matrix form is as follows:

[0101]

[0102] It can be seen that this matrix is ​​not a diagonal matrix. Considering the computational cost, a diagonal matrix should be found to make it still valid. Thus, we get:

[0103]

[0104] Among them, λ 3,max yes The maximum eigenvalue of λ4. When λ4≥2, the above formula always holds true, from which we can get the Lipschitz constant L of the f function f :

[0105] L f =diag(λ 3,max I,λ4I,λ4I) (15)

[0106] By enlarging the formula, we can get a new optimization problem:

[0107]

[0108] in, At this point, the optimization problem can be decomposed into two independent sub-problems:

[0109]

[0110]

[0111] in Cartoon Part x C Updated as follows:

[0112]

[0113]

[0114] In one embodiment, the auxiliary variable d is updated υ and d h as follows:

[0115]

[0116]

[0117] The obtained auxiliary variables are then updated through the proximal function to obtain the following results:

[0118]

[0119]

[0120] During this period, the acceleration strategy introduced into the generalized accelerated proximal gradient method is as follows:

[0121]

[0122]

[0123]

[0124]

[0125] S140: Determine a reconstructed image according to the updated cartoon part and texture part.

[0126] In the specific implementation, use The accurate reconstructed image x can be obtained.

[0127] The compressed sensing image reconstruction method provided by the embodiment of the present invention, with the help of the cartoon texture decomposition model, proposes to use the isotropic total variation image restoration definition to reconstruct the cartoon part of the natural image, and uses a convolutional dictionary learning model based on non-convex optimization to reconstruct the texture part of the natural image, thus overcoming the defects of using the CSC model to represent the entire natural image. Experimental results show that the designed model can effectively reconstruct the different components of the natural image more accurately and obtain a higher quality reconstructed image.

[0128] like Figure 2 As shown, it shows a schematic diagram of the structure of a compressed sensing image reconstruction device in an embodiment of the present invention. The device 200 may include:

[0129] The acquisition unit 210 is used to acquire a cartoon texture decomposition model of the image to be reconstructed, wherein the cartoon texture decomposition model includes a cartoon part and a texture part; the cartoon part is modeled by using an isotropic total variation image restoration definition method; and the texture part is modeled by using a convolution dictionary learning model based on non-convex optimization;

[0130] The optimization unit 220 is used to introduce auxiliary parameters to expand the regularization term of the cartoon part using isotropic total variation norm prior knowledge to obtain an optimization model;

[0131] An updating unit 230, used to update the sparse coefficients and texture dictionary of the texture part in the optimization model, and to update the smoothing parameters and auxiliary parameters of the cartoon part in the optimization model;

[0132] The determination unit 240 is used to determine a reconstructed image according to the updated cartoon part and texture part.

[0133] Among them, the cartoon texture decomposition model is:

[0134]

[0135] Among them, Φ∈RM×N represents the measurement matrix, Represents the texture part of the image to be reconstructed, D L ∈R n×m Represents the texture dictionary, {α i}∈R m represents the corresponding sparse coefficient, Indicates that D L α i Place it at the i-th position and fill the rest with zeros; x C ∈R N Represents the cartoon part of the image to be reconstructed, which is modeled using the isotropic total variation image restoration definition method, with ||x C || TV represents; λ1,λ2,λ3 represent the regularization term coefficients; b is the initial input data, Ω1(x)=||x||0, representing a zero sparsity constraint. And Ω2 is in the form of an indicator function, expressed as: The set C is a unit norm ball used to limit the length of dictionary elements, which means that for D L Any column D L [:,j] satisfies

[0136] The optimization unit 220 is specifically used for:

[0137] The regularization term of the cartoon component of the cartoon texture decomposition model is expanded using the isotropic total variation norm prior knowledge to obtain an optimized model, including:

[0138] Introduce the isotropic total variation image restoration definition method and introduce two auxiliary variables d υ and d h Get the optimized model:

[0139]

[0140] where d υ =D υ x C , d h =D h x C .

[0141] Optionally, the updating unit 230 is further configured to:

[0142] Update the sparse coefficients of the texture part of the optimization model, including:

[0143] make

[0144] {α i} is considered as the following issue:

[0145]

[0146] The proximal gradient algorithm is used to calculate the sparse coefficients {α i} is updated, and the sparse coefficient after update is:

[0147]

[0148] Among them, η1 is the step size,

[0149] Optionally, the updating unit 230 is further configured to:

[0150] Update the dictionary of the texture part of the optimized model, including:

[0151]

[0152] According to Kronecker's product property, we can solve:

[0153]

[0154] Optionally, the updating unit 230 is further configured to:

[0155] Update the smooth variables of the cartoon part in the optimization model and regard it as the following optimization problem:

[0156]

[0157] Further relaxing the equality constraints of the above formula yields:

[0158]

[0159]

[0160] in is a convex set, μ represents the relaxation parameter. Definition and as follows:

[0161]

[0162]

[0163] in, is a continuously differentiable function that satisfies the following descent theorem:

[0164]

[0165] This definition applies to the generalized accelerated proximal gradient method used in this method. f Represents the Lipschitz constant. According to the definition of the Lipschitz constant, we can get L f=H(f), H(f) is the Hessian matrix of the function, and the matrix form is as follows:

[0166]

[0167] It can be seen that this matrix is ​​not a diagonal matrix. Considering the computational cost, a diagonal matrix should be found to make it still valid. Thus, we get:

[0168]

[0169] Among them, λ 3,max yes The maximum eigenvalue of λ4. When λ4≥2, the above formula always holds true, from which we can get the Lipschitz constant L of the f function f :

[0170] L f =diag(λ 3,max I,λ4I,λ4I) (43)

[0171] By enlarging the formula, we can get a new optimization problem:

[0172]

[0173] in, At this point, the optimization problem can be decomposed into two independent sub-problems:

[0174]

[0175]

[0176] in The cartoon part is updated as follows:

[0177]

[0178]

[0179] Optionally, the updating module 230 is further configured to:

[0180] Update the auxiliary variable d of the cartoon part v and d h , as the following problem:

[0181]

[0182]

[0183] The obtained auxiliary variables are then updated through the proximal function to obtain the following results:

[0184]

[0185]

[0186] Optionally, the updating unit 230 is further configured to:

[0187] The acceleration strategy in the generalized accelerated proximal gradient method is introduced to accelerate the convergence speed of the optimization model, including:

[0188]

[0189]

[0190]

[0191]

[0192] As for the compressed sensing image reconstruction device of the embodiment of the present invention, since it corresponds to the compressed sensing image reconstruction method in the above embodiment, the description is relatively simple. For relevant similarities, please refer to the description of the compressed sensing image reconstruction method in the above embodiment, which will not be described in detail here.

[0193] Figure 3 FIG. 1 is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. Figure 3 As shown, a schematic diagram of the structure of an electronic device 300 suitable for implementing an embodiment of the present invention is shown. The electronic device 300 includes a central processing unit (CPU) 301, which can execute a program corresponding to the compressed sensing image reconstruction method stored in a read-only memory (ROM) 302 or execute a corresponding program of the compressed sensing image reconstruction method loaded from a storage part 308 to a random access memory (RAM) 303. In the RAM 303, various data and programs required by the electronic device 300 are also stored. The CPU 301, the ROM 302, and the RAM 303 are connected to each other via a bus 304. An input / output (I / O) interface 305 is also connected to the bus 304.

[0194] The following components are connected to the I / O interface 305: an input section 306 including a keyboard, a mouse, etc.; an output section 307 including a cathode ray tube (CRT), a liquid crystal display (LCD), etc., and a speaker, etc.; a storage section 308 including a hard disk, etc.; and a communication section 309 including a network interface card such as a LAN card, a modem, etc. The communication section 309 performs communication processing via a network such as the Internet. A drive 310 is also connected to the I / O interface 306 as needed. A removable medium 311, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 310 as needed, so that a computer program read therefrom is installed into the storage section 308 as needed.

[0195] In particular, according to the embodiments of the present disclosure, the above reference Figure 1 The described process can be implemented as a computer software program. For example, an embodiment of the present disclosure includes a computer program product, which includes a computer program tangibly contained on a machine-readable medium, and the computer program includes program code for performing the above-mentioned compressed sensing image reconstruction method. In such an embodiment, the computer program can be downloaded and installed from a network through the communication part 309, and / or installed from a removable medium 311.

[0196] In the several embodiments provided by the present invention, it should be understood that the disclosed technical content can be implemented in other ways. Among them, the device embodiments described above are only schematic. For example, the division of the units can be a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of units or modules, which can be electrical or other forms.

[0197] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple units. Some or all of the units may be selected according to actual needs to achieve the purpose of the present embodiment.

[0198] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0199] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, a server or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), mobile hard disk, magnetic disk or optical disk and other media that can store program codes.

[0200] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A compressed sensing image reconstruction method, characterized in that: The method comprises: Obtaining a cartoon texture decomposition model of the image to be reconstructed, the cartoon texture decomposition model comprising a cartoon part and a texture part; the cartoon part is modeled using an isotropic total variation image restoration definition method; the texture part is modeled using a convolutional dictionary learning model based on non-convex optimization; Auxiliary parameters are introduced to expand the regularization term of the cartoon part using isotropic total variation norm prior knowledge to obtain an optimization model; Respectively updating the sparse coefficients and texture dictionary of the texture part in the optimization model, and respectively updating the smooth parameters and auxiliary parameters of the cartoon part in the optimization model; According to the updated cartoon section and texture section, use Determine the reconstructed image, where x is the reconstructed image, Indicates that D L α i Place it at the i-th position and fill the rest with zeros; D L is the updated texture dictionary, α i is the updated sparse, x C For the updated cartoon section; The cartoon texture decomposition model is: Among them, Φ∈R M×N represents the measurement matrix, Represents the texture part of the image to be reconstructed, D L ∈R n×m Represents the texture dictionary, {α i }∈R m represents the corresponding sparse coefficient, Indicates that D L α i Place it at the i-th position and fill the rest with zeros; x C ∈R N Represents the cartoon part of the image to be reconstructed, and is modeled using the isotropic total variation image restoration definition method, with ‖x C ‖ TV represents; λ1,λ2,λ3 represent the regularization term coefficients; b is the initial input data, Ω1(x)=‖x‖0, representing a zero sparsity constraint; Ω2 is in the form of an indicator function, expressed as: Among them, the set C is a unit norm ball used to limit the length of dictionary elements, which means that for D L Any column D L [:,j] satisfies The optimization function is: Among them, d υ and d h is an auxiliary variable; d υ =D υ x C , d h =D h x C .

2. The method according to claim 1, characterized in that Updating the sparse coefficient of the texture part in the optimization model includes: The update of sparse coefficients is regarded as a convolutional basis pursuit denoising problem; The proximal gradient descent algorithm is used to solve the convolutional basis pursuit denoising problem and obtain the updated sparse coefficients: Among them, η1 is the step size, 3. The method according to claim 1, characterized in that Updating the texture dictionary of the texture part in the optimization model includes: Update the texture dictionary to: in, Solve according to Kronecker's property.

4. The method according to claim 1, characterized in that The smoothing parameters of the cartoon part in the optimization model are updated, including: The smoothing parameter x C The update of is considered as an optimization problem: in, η4=λ4 -1 ;d υ and d h is an auxiliary variable; μ represents the relaxation parameter; B is a convex set; λ 3,max yes The maximum eigenvalue of The generalized accelerated proximal gradient method is used to solve the optimization problem and obtain the updated smoothing parameter x C : Among them, the acceleration strategies of the generalized accelerated proximal gradient method include: definition and as follows: in, is a continuously differentiable function; prox is the proximal function.

5. The method according to claim 1, characterized in that: Update the auxiliary parameter d of the cartoon part in the optimization model υ , d h ,include: Update auxiliary variable d υ and d h for: Among them, prox is the proximal function.

6. A compressed sensing image reconstruction device, characterized in that: The device comprises: An acquisition unit is used to acquire a cartoon texture decomposition model of an image to be reconstructed, wherein the cartoon texture decomposition model includes a cartoon part and a texture part; the cartoon part is modeled by using an isotropic total variation image restoration definition method; the texture part is modeled by using a convolution dictionary CDL learning model based on non-convex optimization; An optimization unit is used to introduce auxiliary parameters to expand the regularization term of the cartoon part using isotropic total variation total variation norm prior knowledge to obtain an optimization model; An updating unit, used to update the sparse coefficients and texture dictionary of the texture part in the optimization model, and to update the smoothing parameters and auxiliary parameters of the cartoon part in the optimization model; A determination unit, used for determining a reconstructed image according to the updated cartoon part and texture part; The cartoon texture decomposition model is: Among them, Φ∈R M×N represents the measurement matrix, Represents the texture part of the image to be reconstructed, D L ∈R n×m Represents the texture dictionary, {α i }∈R m represents the corresponding sparse coefficient, Indicates that D L α i Place it at the i-th position and fill the rest with zeros; x C ∈R N Represents the cartoon part of the image to be reconstructed, and is modeled using the isotropic total variation image restoration definition method, with ‖x C ‖ TV represents; λ1,λ2,λ3 represent the regularization term coefficients; b is the initial input data, Ω1(x)=‖x‖0, representing a zero sparsity constraint; Ω2 is in the form of an indicator function, expressed as: Among them, the set C is a unit norm ball used to limit the length of dictionary elements, which means that for D L Any column D L [:,j] satisfies The optimization function is: Among them, d υ and d h is an auxiliary variable; d υ =D υ x C , d h =D h x C .

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the compressed sensing image reconstruction method according to any one of claims 1 to 5 is implemented.

8. A computer-readable storage medium, wherein a computer instruction set is stored in the computer-readable storage medium, and when the computer instruction set is executed by a processor, the compressed sensing image reconstruction method according to any one of claims 1 to 5 is implemented.

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