Computed tomography (CT) reconstruction method and system based on tight frame wavelet transform and image gradient

Abstract

The invention provides a CT reconstruction method and system based on tight frame wavelet transform and image gradient, and relates to the technical field of image processing, and the method comprises the steps: obtaining a prior image and sparse angle CT projection data of a target object; based on a prior image of a target object, establishing an optimization model of sparse constraint of a tight frame wavelet frequency domain coefficient; solving the sparse constraint optimization model of the tight frame wavelet frequency domain coefficient to obtain an optimal tight frame wavelet frequency domain coefficient; based on the sparse angle CT projection data and the optimal tight frame wavelet frequency domain coefficient, establishing a dual regularization CT reconstruction optimization model; and solving the dual regularization CT reconstruction optimization model, and outputting a reconstructed CT image. According to the method provided by the invention, by establishing a dual regularization CT reconstruction optimization model of tight frame wavelet transform domain prior and image gradient sparse features, strip artifacts and noise appearing in the sparse angle CT image can be effectively inhibited, the quality of the reconstructed image is greatly improved, and the clinical diagnosis quality is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of image processing in hospital images, and in particular relates to a CT reconstruction method and system based on tight frame wavelet transform and image gradient. Background Art

[0002] CT is a technology widely used in hospital imaging diagnosis. It reconstructs high-resolution images of the internal structure of a target object by acquiring projection data from multiple angles. However, in sparse angle CT scanning, due to the incompleteness of projection data, the reconstructed CT images often contain stripe artifacts and noise, which seriously affects the image quality and the accuracy of clinical diagnosis.

[0003] In order to solve this problem, researchers have proposed a variety of CT reconstruction methods. Among them, the reconstruction method based on regularization has achieved good results in suppressing artifacts and noise. The regularization method introduces prior knowledge and imposes constraints on the reconstruction process, thereby improving image quality. However, the existing regularization reconstruction method still has certain limitations. On the one hand, the traditional wavelet transform regularization method has limited effect in dealing with strip artifacts and noise; on the other hand, the existing method does not make sufficient use of image gradients during the reconstruction process, resulting in the loss of edge information of the reconstructed image. Summary of the invention

[0004] The purpose of the present invention is to provide a CT reconstruction method and system based on tight frame wavelet transform and image gradient in view of the problems existing in the prior art. Based on sparse angle CT projection data and tight frame wavelet frequency domain coefficients, a dual regularization CT reconstruction optimization model is established, which can effectively suppress the strip artifacts and noise appearing in sparse angle CT images, greatly improve the quality of reconstructed images, and improve the quality of clinical diagnosis.

[0005] According to one aspect of the present invention, a CT reconstruction method based on tight frame wavelet transform and image gradient is provided, comprising the following steps:

[0006] S1: Acquire a priori image and sparse angular CT projection data of the target object;

[0007] S2: Based on the prior image of the target object, an optimization model with tight frame wavelet frequency domain coefficient sparse constraints is established;

[0008] S3: solving the optimization model of the tight frame wavelet frequency domain coefficient sparse constraint to obtain the optimal tight frame wavelet frequency domain coefficient;

[0009] S4: Based on the sparse angular CT projection data, a target object image domain gradient sparse regularization constraint is designed, and combined with the optimal tight frame wavelet frequency domain coefficient, a dual regularization CT reconstruction optimization model is established;

[0010] S5: Solving the dual regularized CT reconstruction optimization model, and outputting a reconstructed CT image based on the solution result.

[0011] Furthermore, the S1 is specifically:

[0012] Obtain the target object's previous CT reconstruction image of the same part as the prior image , CT projection data acquired through sparse angle CT scanning protocol .

[0013] Furthermore, the S2 is specifically:

[0014] Tight Frame Wavelet Transform For the prior image Transform to obtain the tight frame wavelet frequency domain coefficients ;

[0015] For the prior image In the frequency domain, the coefficients of the tight frame wavelet Perform L0 sparse regularization constraints and establish the optimization model of tight frame wavelet frequency domain coefficient sparse constraints as follows:

[0016]

[0017] in, is a tight frame wavelet transform of the target object satisfying the L0 sparse regularization constraint The frequency domain coefficients of is the optimal tight frame wavelet frequency domain coefficient obtained by solving the optimization model, is a regularization parameter greater than 0, is the index of the frequency domain subband, is a two-dimensional vector of frequency subbands The number of non-zero values ​​of .

[0018] Furthermore, the S3 is specifically:

[0019] The hard threshold method is used to solve the optimization model of the tight frame wavelet frequency domain coefficient sparse constraint to obtain the optimal tight frame wavelet frequency domain coefficient:

[0020]

[0021] in, , the hard threshold function is .

[0022] Furthermore, the S4 is specifically:

[0023] Based on sparse angular CT projection data acquired by S1 , design a target object image domain gradient sparse regularization constraint , so that when reconstructing the target object image, the gradient of the target object image exhibits a sparse characteristic;

[0024] Introduce an L1-based residual regularization term , used to constrain the tight frame wavelet frequency domain coefficients so that they approximate the optimal tight frame wavelet frequency domain coefficients;

[0025] Combining the sparse regularization constraint of the target object image domain gradient and the frequency domain coefficients under the tight frame wavelet transform, as well as the characteristics of the optimal tight frame wavelet frequency domain coefficient approximation, a dual regularization CT reconstruction optimization model is established as follows:

[0026]

[0027] Among them, the matrix A represents Size of CT scanning system matrix, is the number of X-rays, is the number of linear array detector units, is the CT image of the target object to be reconstructed, is the acquired sparse angular CT projection data, is a diagonal matrix whose diagonal elements have values ,and , are regularization parameters, is the L1 residual regularization term, is the image domain gradient sparse regularization constraint.

[0028] Furthermore, the S5 is specifically:

[0029] The double regularized CT reconstruction optimization model described in S4 is solved using the alternating direction multiplier method, and the reconstructed CT image is output based on the solution.

[0030] According to one aspect of the present invention, a regularized CT reconstruction system based on tight frame wavelet transform and image gradient is provided, comprising:

[0031] A data acquisition module, used to acquire a priori images and sparse angular CT projection data of a target object;

[0032] The optimization model building module builds an optimization model with tight frame wavelet frequency domain coefficient sparse constraints based on the prior image;

[0033] Optimization model solving module, used to solve the optimization model of tight frame wavelet frequency domain coefficient sparse constraints;

[0034] Regularized CT reconstruction optimization model building module, which builds a regularized CT reconstruction optimization model based on sparse angular CT projection data and frequency domain coefficients;

[0035] The regularized CT reconstruction optimization model solving and image output module is used to solve the regularized CT reconstruction optimization model and output the reconstructed CT image.

[0036] According to one aspect of the present invention, there is provided an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of a CT reconstruction method based on tight frame wavelet transform and image gradient when executing the computer program.

[0037] According to one aspect of the present invention, a computer-readable storage medium is provided, which stores a computer program. When the computer program is executed by a processor, the steps of the CT reconstruction method based on tight frame wavelet transform and image gradient are implemented.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] 1. The present invention proposes a CT reconstruction method and system based on tight frame wavelet transform and image gradient, which obtains high-quality prior information by performing L0 sparse regularization constraints on the coefficients of the tight frame wavelet frequency domain of the prior image and designs sparse regularization constraints on the gradient of the target object image domain, suppresses the artifacts and noise of the sparse angular CT image, and greatly improves the quality of the reconstructed image, thereby improving the quality of clinical diagnosis;

[0040] 2. The present invention proposes a CT reconstruction method and system based on tight frame wavelet transform and image gradient. By designing the L1 residual regularization term, it is used to constrain the tight frame wavelet frequency domain coefficients so that they are close to the optimal tight frame wavelet frequency domain coefficients, thereby protecting the structure and edge characteristics of the target object. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] 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 only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0042] Figure 1 A flowchart of a CT reconstruction method based on tight frame wavelet transform and image gradient provided by an embodiment of the present invention;

[0043] Figure 2 A structural schematic diagram of a CT reconstruction system based on tight frame wavelet transform and image gradient provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0044] It should be noted that:

[0045] The target object refers to the structure that needs to be analyzed by CT images, and images related to the target object can be regarded as being obtained based on CT image processing.

[0046] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions 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 are within the scope of protection of the present invention.

[0047] like Figure 1 As shown, a flow chart of a CT reconstruction method based on tight frame wavelet transform and image gradient provided by an embodiment of the present invention includes:

[0048] S1: Acquire a priori image and sparse angular CT projection data of the target object;

[0049] S2: Based on the prior image of the target object, an optimization model with tight frame wavelet frequency domain coefficient sparse constraints is established;

[0050] S3: solving the optimization model of the tight frame wavelet frequency domain coefficient sparse constraint to obtain the optimal tight frame wavelet frequency domain coefficient;

[0051] S4: Based on the sparse angular CT projection data, a target object image domain gradient sparse regularization constraint is designed, and combined with the optimal tight frame wavelet frequency domain coefficient, a dual regularization CT reconstruction optimization model is established;

[0052] S5: Solving the dual regularized CT reconstruction optimization model, and outputting a reconstructed CT image based on the solution result.

[0053] Specifically, the S1 is:

[0054] Obtain the target object's previous CT reconstruction image of the same part as the prior image , obtain CT projection data under sparse angle CT scanning protocol , and the system scanning parameters of the CT equipment.

[0055] Specifically, the S2 is:

[0056] Tight Frame Wavelet Transform For the prior image Transform to obtain the tight frame wavelet frequency domain coefficients ;

[0057] To further suppress the prior image The noise and other interference in the image are used to obtain high-quality prior information. In the frequency domain, the coefficients of the tight frame wavelet Perform L0 sparse regularization constraints and establish the optimization model of tight frame wavelet frequency domain coefficient sparse constraints as follows:

[0058] (1)

[0059] in, is a tight frame wavelet transform of the target object satisfying the L0 sparse regularization constraint The frequency domain coefficients of is the optimal tight frame wavelet frequency domain coefficient obtained by solving the optimization model, is a regularization parameter greater than 0, is the index of the frequency domain subband, is a two-dimensional vector of frequency subbands The number of non-zero values ​​of .

[0060] Furthermore, the S3 is specifically:

[0061] The hard threshold method is used to solve the optimization model (1) of the tight frame wavelet frequency domain coefficient sparse constraint, and the optimal tight frame wavelet frequency domain coefficient is obtained. :

[0062] (2)

[0063] in, , the hard threshold function is .

[0064] Specifically, the S4 is as follows:

[0065] Based on sparse angular CT projection data acquired by S1 To suppress artifacts and noise, a sparse regularization constraint is designed for the target object image domain gradient ;

[0066] In order to protect the structure and edge features of the target object, the frequency domain coefficients of the target object under the tight frame wavelet transform are compared with the optimal tight frame wavelet frequency domain coefficients obtained by S2. Perform approximation constraints and design L1 residual regularization terms ;

[0067] Combining the target object image domain gradient sparse regularization constraint with the frequency domain coefficients under the tight frame wavelet transform, and the optimal tight frame wavelet frequency domain coefficients Based on the characteristics of the approximation, a dual regularized CT reconstruction optimization model is established as follows:

[0068] (3)

[0069] Among them, the matrix A represents Size of CT scanning system matrix, is the number of X-rays, is the number of linear array detector units, is the CT image of the target to be reconstructed, is the acquired sparse angular CT projection data, is a diagonal matrix whose diagonal elements have values ,and , are regularization parameters, is the L1 residual regularization term, is the image domain gradient sparse regularization constraint.

[0070] Specifically, the S5 is as follows:

[0071] First, based on the dual regularized CT reconstruction optimization model (3), two intermediate variables are introduced: and , establish the optimization problem with equality constraints as follows:

[0072] (4)

[0073] By using the augmented Lagrange multiplier method, the Lagrange multiplier is introduced to transform the above optimization problem (4) with equality constraints into an unconstrained optimization problem as follows:

[0074] (5)

[0075] in and is a positive parameter, and is the dual variable. The alternating direction multiplier method is used to solve the above unconstrained optimization problem (5). The iterative formula is as follows:

[0076]

[0077] To avoid calculating the system matrix The inverse of , choose to use the gradient descent method to solve the above iterative formula (6), and use ,get:

[0078] (7)

[0079] Using the soft threshold method to solve the above formula (7), we can get The formula is as follows:

[0080] (8)

[0081] Among them, soft() is a function that implements soft threshold operation;

[0082] Using the ROF method, solve the above formula (6.3);

[0083] Among them, the ROF method is the Rudin-Osher-Fatemi (ROF) model, a mathematical model for image denoising;

[0084] Finally, when the iterative formula of equation (6) converges, the reconstructed CT image is output.

[0085] The implementation basis of each embodiment of the present invention is to implement programmed processing through a device with a processor function. Therefore, in engineering practice, the technical solutions and functions of each embodiment of the present invention are encapsulated into various modules. Based on this reality, on the basis of the above embodiments, an embodiment of the present invention provides a CT reconstruction system based on a tight frame wavelet transform and image gradient, which is used to execute a CT reconstruction method based on a tight frame wavelet transform and image gradient in the above method embodiment.

[0086] See also Figure 2 The system comprises:

[0087] A data acquisition module, used to acquire a priori images and sparse angular CT projection data of a target object;

[0088] The optimization model building module builds an optimization model with tight frame wavelet frequency domain coefficient sparse constraints based on the prior image;

[0089] Optimization model solving module, used to solve the optimization model of tight frame wavelet frequency domain coefficient sparse constraints;

[0090] Regularized CT reconstruction optimization model building module, which builds a regularized CT reconstruction optimization model based on sparse angular CT projection data and frequency domain coefficients;

[0091] The regularized CT reconstruction optimization model solving and image output module is used to solve the regularized CT reconstruction optimization model and output the reconstructed CT image.

[0092] An embodiment of the present invention provides a regularized CT reconstruction system based on tight frame wavelet transform and image gradient, and the specific implementation process thereof includes: firstly starting the system and entering the data acquisition module, acquiring a priori image of the target object from a database or a device, performing a sparse angle CT scan on the prior image, and acquiring sparse angle CT projection data; based on the acquired prior image, establishing an optimization model of tight frame wavelet frequency domain sparse constraints, solving the optimization model using a hard threshold method, and calculating tight frame wavelet frequency domain coefficients; based on the acquired sparse angle CT projection data and the calculated frequency domain coefficients, establishing a regularized CT reconstruction optimization model, and solving the regularized CT reconstruction optimization model; finally, outputting the reconstructed CT image, saving it in a specified format, ending the processing, and closing the system.

[0093] The embodiment of the present invention provides a CT reconstruction system based on tight frame wavelet transform and image gradient, using Figure 2 Several modules in the proposed method obtain high-quality prior information by performing L0 sparse regularization constraints on the coefficients of the prior image in the tight frame wavelet frequency domain and designing gradient sparse regularization constraints in the target object image domain. This suppresses artifacts and noise in sparse angular CT images, greatly improves the quality of reconstructed images, and improves the quality of clinical diagnosis.

[0094] Based on the same inventive concept as the aforementioned embodiment, an embodiment of the present invention further provides an electronic device, including a memory and a processor, the memory being used to store computer executable instructions, and the processor being used to execute computer executable instructions, to implement a CT reconstruction method based on tight frame wavelet transform and image gradient as proposed in the aforementioned embodiment.

[0095] This embodiment also provides a computer-readable storage medium, which stores a computer program. When the program is executed by the processor, it is used to suppress the CT prior image, improve the quality of the reconstructed CT image, and protect the structure and edge features of the target object. The storage medium can be any non-volatile storage device such as a hard disk, a solid-state hard disk, a flash disk, an optical disk, etc., which is used to store computer program codes and necessary data files. The stored computer program includes: a data acquisition module, an optimization model establishment module, an optimization model solution module, a regularized CT reconstruction optimization model establishment module, a regularized CT reconstruction optimization model solution and an image output module.

[0096] Finally, it should be pointed out that the above specific embodiments are only representative examples of the present invention. Obviously, the present invention is not limited to the above specific embodiments, and there are many variations. Any simple modification, equivalent changes and modifications made to the above specific embodiments based on the technical essence of the present invention should be considered to belong to the protection scope of the present invention.

Claims

1. A CT reconstruction method based on tight frame wavelet transform and image gradient, characterized in that: The following steps are involved: S1: Acquire a priori image and sparse angular CT projection data of the target object; S2: Based on the prior image of the target object, an optimization model with tight frame wavelet frequency domain coefficient sparse constraints is established; S3: solving the optimization model of the tight frame wavelet frequency domain coefficient sparse constraint to obtain the optimal tight frame wavelet frequency domain coefficient; S4: Based on the sparse angular CT projection data, a target object image domain gradient sparse regularization constraint is designed, and combined with the optimal tight frame wavelet frequency domain coefficient, a dual regularization CT reconstruction optimization model is established; S5: Solving the dual regularized CT reconstruction optimization model, and outputting a reconstructed CT image based on the solution result.

2. The CT reconstruction method based on tight frame wavelet transform and image gradient according to claim 1, characterized in that: The S1 is specifically: A previous CT image of the target object is obtained as a priori image, and sparse angle CT projection data is obtained through sparse angle CT scanning.

3. The CT reconstruction method based on tight frame wavelet transform and image gradient according to claim 1, characterized in that: The S2 is specifically: The prior image is transformed by using tight frame wavelet transform to obtain tight frame wavelet frequency domain coefficients; The L0 sparse regularization constraint is applied to the tight frame wavelet frequency domain coefficients of the prior image, and the optimization model of the tight frame wavelet frequency domain coefficient sparse constraint is established as follows: ， in, is a tight frame wavelet transform of the target object satisfying the L0 sparse regularization constraint The frequency domain coefficients of is the optimal tight frame wavelet frequency domain coefficient obtained by solving the optimization model, is a regularization parameter greater than 0, is the index of the frequency domain subband, is a two-dimensional vector of frequency subbands The number of non-zero values ​​of .

4. The CT reconstruction method based on tight frame wavelet transform and image gradient according to claim 1, characterized in that: The S3 is specifically: The hard threshold method is used to solve the optimization model of the tight frame wavelet frequency domain coefficient sparse constraint to obtain the optimal tight frame wavelet frequency domain coefficient: ， in, , the hard threshold function is .

5. The CT reconstruction method based on tight frame wavelet transform and image gradient according to claim 1, characterized in that: The S4 is specifically: Based on the sparse angular CT projection data obtained by S1, a target object image domain gradient sparse regularization constraint is designed so that when the target object image is reconstructed, the gradient of the target object image presents a sparse characteristic; An L1-based residual regularization term is introduced to constrain the tight frame wavelet frequency domain coefficients so that they are close to the optimal tight frame wavelet frequency domain coefficients. Combining the sparse characteristics of the target object image domain gradient and the tight frame wavelet frequency domain coefficients, as well as the characteristics of the optimal tight frame wavelet frequency domain coefficient approximation, a dual regularized CT reconstruction optimization model is established as follows: ， Among them, the matrix A represents Size of CT scanning system matrix, is the number of X-rays, is the number of linear array detector units, is the CT image of the target object to be reconstructed, is the acquired sparse angular CT projection data, is a diagonal matrix whose diagonal elements have values ,and , are regularization parameters, is the L1 residual regularization term, is the image domain gradient sparse regularization constraint.

6. The CT reconstruction method based on tight frame wavelet transform and image gradient according to claim 1, characterized in that: The S5 is specifically: The double regularized CT reconstruction optimization model described in S4 is solved using the alternating direction multiplier method, and the reconstructed CT image is output based on the solution.

7. A CT reconstruction system based on tight frame wavelet transform and image gradient, characterized in that: include: A data acquisition module, used to acquire a priori images and sparse angular CT projection data of a target object; The optimization model building module builds an optimization model with tight frame wavelet frequency domain coefficient sparse constraints based on the prior image; Optimization model solving module, used to solve the optimization model of tight frame wavelet frequency domain coefficient sparse constraints; Regularized CT reconstruction optimization model building module, which builds a regularized CT reconstruction optimization model based on sparse angular CT projection data and frequency domain coefficients; The regularized CT reconstruction optimization model solving and image output module is used to solve the regularized CT reconstruction optimization model and output the reconstructed CT image.

8. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the CT reconstruction method based on tight frame wavelet transform and image gradient according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the CT reconstruction method based on tight frame wavelet transform and image gradient according to any one of claims 1 to 6 are implemented.

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