Limited angle CT (Computed Tomography) iterative reconstruction method and system based on tight frame wavelet transform

Abstract

The invention provides a finite angle CT iterative reconstruction method and system based on tight frame wavelet transform, and relates to the technical field of image processing, and the method comprises the steps: obtaining a pre-image and finite angle CT projection data of a to-be-detected object; total variation regularization constraint is carried out based on the pre-image of the to-be-detected object, and an initial optimization model is established; solving the initial optimization model to obtain a high-quality pre-CT image, and performing transformation by adopting tight frame wavelet transform to obtain a tight frame wavelet frequency domain coefficient; based on limited angle CT projection data and a to-be-detected object before reconstruction, a dual regularization CT reconstruction optimization model is established in combination with the tight frame wavelet transform frequency domain coefficient; and solving the dual regularization CT reconstruction optimization model, and outputting a reconstructed CT image. According to the method, the double regularization CT reconstruction optimization model of the tight frame wavelet transform domain sparse characteristic finite angle is established, strip artifacts and noise appearing in the finite angle CT image can be effectively restrained, 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 imaging, and particularly relates to a limited-angle CT iterative reconstruction method and system based on tight-frame wavelet transform. Background Art

[0002] Computed tomography (CT) is an imaging technology widely used in the medical field. It reconstructs a detailed image of the internal structure of an object under examination by capturing X-ray projections from multiple angles. Although CT technology plays an important role in medical diagnosis, in limited-angle CT scans, due to incomplete projection data obtained, the reconstructed images often have obvious streak artifacts and noise, which seriously reduce the image quality and thus affect the accuracy of clinical diagnosis.

[0003] In response to this challenge, researchers have developed various CT image reconstruction techniques. Among these techniques, regularization-based reconstruction methods have received attention due to their effectiveness in reducing artifacts and noise. Regularization techniques enhance image quality by integrating prior information and imposing additional constraints on the reconstruction process. Nevertheless, existing regularization reconstruction techniques still have some deficiencies. On the one hand, traditional wavelet transform-based regularization methods are not ideal in eliminating streak artifacts and noise; on the other hand, existing techniques fail to fully utilize image gradient information during the reconstruction process, resulting in the loss of edge details in the reconstructed images.

[0004] Therefore, it is necessary to develop a limited-angle CT iterative reconstruction method and system based on tight-frame wavelet transform that can effectively suppress artifacts and noise while retaining the edge information of the image to address the above problems. Summary of the Invention

[0005] The object of the present invention is to address the problems existing in the prior art and provide a limited-angle CT iterative reconstruction method and system based on tight-frame wavelet transform. Based on limited-angle CT projection data and tight-frame wavelet frequency-domain coefficients, a dual-regularized CT reconstruction optimization model is established, which can effectively suppress the streak artifacts and noise in limited-angle CT images, significantly improve the quality of the reconstructed images, and enhance the quality of clinical diagnosis.

[0006] According to one aspect of the specification of the present invention, a limited-angle CT iterative reconstruction method based on tight-frame wavelet transform is provided, including the following steps:

[0007] Data acquisition, obtaining a pre-image of the object to be detected and limited-angle CT projection data;

[0008] Initial model optimization, performing total variation regularization constraint based on the pre-image of the object to be detected to construct an initial optimization model;

[0009] Image optimization: Solve the initial optimization model to obtain high-quality pre-CT images, and perform wavelet transform on the high-quality pre-CT images using the tight-frame wavelet transform to obtain the tight-frame wavelet frequency domain coefficients;

[0010] Dual regularization model construction: Based on the limited-angle CT projection data and the object to be detected before reconstruction, combined with the tight-frame wavelet transform frequency domain coefficients, establish a dual regularization CT reconstruction optimization model;

[0011] Image reconstruction: Solve the dual regularization CT reconstruction optimization model, and output the CT image of the object to be detected after reconstruction based on the solution results.

[0012] Furthermore, the data acquisition is specifically as follows:

[0013] Obtain the pre-image of the object to be detected at the same position in the early stage as the pre-image , and obtain the CT projection data through the limited-angle CT scanning protocol .

[0014] Furthermore, the initial optimization of the model is specifically as follows:

[0015] Perform total variation regularization constraint on the pre-image to establish the following optimization model:

[0016]

[0017] Where, is the pre-image, is the object to be detected before reconstruction, is the high-quality pre-CT image obtained by solving the optimization model, is a regularization parameter greater than 0, is the total variation regularization constraint.

[0018] Furthermore, the image optimization is specifically as follows:

[0019] Use the tight-frame wavelet transform to transform the high-quality pre-CT image obtained by solving the optimization model, and obtain the tight-frame wavelet frequency domain coefficients , and the formula is as follows:

[0020]

[0021] Where, is the index of the frequency sub-band, is the tight-frame wavelet transform.

[0022] Furthermore, the construction of the dual regularization model is specifically as follows:

[0023] Based on the limited-angle CT projection data obtained by data acquisition, design the sparse regularization constraint of the object to be detected in the tight-frame wavelet frequency domain ;

[0024] Introduce an L1-based residual regularization term to perform approximation constraint on the frequency-domain coefficients of the object to be detected before reconstruction under the tight-frame wavelet transform and the tight-frame wavelet frequency-domain coefficients ;

[0025] Combine the sparse characteristics of the tight-frame wavelet frequency domain of the object to be detected before reconstruction and the characteristics of the similarity between the frequency-domain coefficients under the tight-frame wavelet transform and the tight-frame wavelet frequency-domain coefficients to establish the following dual-regularized CT reconstruction optimization model:

[0026]

[0027] where the matrix A represents the CT scanning system matrix of size the number of X-rays, the size of is equal to the number of pixels of the image after reconstruction, is the CT image of the object to be detected before reconstruction, is the limited-angle CT projection data obtained, is a diagonal matrix, the values of whose diagonal elements are and , are all regularization parameters, is the L1 residual regularization term, is the image-domain gradient sparse regularization constraint.

[0028] Furthermore, the image reconstruction is specifically:

[0029] Use the alternating direction multiplier method to solve the dual-regularized CT reconstruction optimization model, and output the reconstructed CT image based on the obtained result.

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

[0031] A data acquisition module for acquiring a pre-image of the object to be detected and limited-angle CT projection data;

[0032] An initial optimization model construction module for performing total variation regularization constraint based on the pre-image of the object to be detected and constructing an optimization model;

[0033] An image optimization module for solving the optimization model to obtain a high-quality pre-CT image, performing a transform on the high-quality pre-CT image using the tight-frame wavelet transform to obtain tight-frame wavelet frequency-domain coefficients;

[0034] A dual regularization model construction module, configured to establish a dual regularization CT reconstruction optimization model based on the limited-angle CT projection data and the object to be detected before reconstruction, in combination with the frequency-domain coefficients of the tight-frame wavelet transform;

[0035] An image reconstruction module, configured to solve the regularized CT reconstruction optimization model and output a CT image of the object to be detected after reconstruction.

[0036] According to one aspect of the specification of the present invention, there is provided an electronic device, including a memory and a processor, where the memory stores a computer program, and when the processor executes the computer program, the steps of the method for iterative reconstruction of limited-angle CT based on tight-frame wavelet transform are implemented.

[0037] According to one aspect of the specification of the present invention, there is provided a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the method for iterative reconstruction of limited-angle CT based on tight-frame wavelet transform are implemented.

[0038] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0039] 1. For the method and system for iterative reconstruction of limited-angle CT based on tight-frame wavelet transform proposed by the present invention, by performing total variation regularization constraint on the pre-image, an optimization model is established and a high-quality pre-image is obtained, suppressing the artifacts and noise of the limited-angle CT image, greatly improving the quality of the reconstructed image, and thus improving the clinical diagnosis quality;

[0040] 2. For the method and system for iterative reconstruction of limited-angle CT based on tight-frame wavelet transform proposed by the present invention, by designing an L1 residual regularization term, which is used to constrain the frequency-domain coefficients under the tight-frame wavelet transform to approximate the tight-frame wavelet frequency-domain coefficients, protecting the features such as the structure and edges of the object to be detected. Description of the Drawings

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention, and for those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0042] Figure 1 It is a schematic flowchart of a method for iterative reconstruction of limited-angle CT based on tight-frame wavelet transform provided by an embodiment of the present invention;

[0043] Figure 2 It is a schematic diagram of the modules of a CT reconstruction system based on tight-frame wavelet transform and image gradient provided by an embodiment of the present invention. Detailed implementation manners

[0044] It should be noted that:

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

[0046] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0047] As Figure 1 shown, a flowchart of a limited-angle CT iterative reconstruction method based on tight-frame wavelet transform provided by an embodiment of the present invention includes: obtaining a pre-image of the object to be detected and limited-angle CT projection data; performing total variation regularization constraint based on the pre-image of the object to be detected to construct an initial optimization model; solving the initial optimization model to obtain a high-quality pre-CT image, and performing a transform on the high-quality pre-CT image by using tight-frame wavelet transform to obtain tight-frame wavelet frequency domain coefficients; based on the limited-angle CT projection data and the object to be detected before reconstruction, combining the tight-frame wavelet transform frequency domain coefficients, establishing a double-regularization CT reconstruction optimization model; solving the double-regularization CT reconstruction optimization model, and outputting a CT image of the object to be detected after reconstruction based on the solution result.

[0048] Specifically, obtain a CT reconstruction image of the same part of the object to be detected in the early stage as the pre-image , and obtain CT projection data under a limited-angle CT scanning protocol , as well as the system scanning parameters of the CT device.

[0049] Specifically, to further suppress noises and other interferences existing in the pre-image , obtain high-quality pre-information, perform total variation regularization constraint on the pre-image , and establish the following initial optimization model:

[0050] (1)

[0051] Wherein, is the pre-image, is the object to be detected after reconstruction, is the high-quality pre-CT image obtained by solving the initial optimization model, is a regularization parameter greater than 0, is the total variation regularization constraint.

[0052] Specifically, the high-quality pre-CT image is transformed using the tight-frame wavelet transform, and the tight-frame wavelet frequency-domain coefficients are obtained. The formula is as follows:

[0053] (2)

[0054] Where is the index of the frequency-domain subband, and is the tight-frame wavelet transform.

[0055] Specifically, using the limited-angle CT projection data obtained by data acquisition , to suppress artifacts and noise, a sparse regularization constraint of the object to be detected in the tight-frame wavelet frequency domain before reconstruction is designed ; to protect the structure and edges and other features of the object to be detected before reconstruction, the frequency-domain coefficients of the object to be detected under the tight-frame wavelet transform are approximated and constrained with the tight-frame wavelet frequency-domain coefficients obtained by image optimization ; design the corresponding L1 residual regularization term ; combining the sparse characteristics of the object to be detected in the tight-frame wavelet frequency domain before reconstruction with the characteristics that the frequency-domain coefficients under the tight-frame wavelet transform are similar to the tight-frame wavelet frequency-domain coefficients , the following dual-regularized CT reconstruction optimization model is established:

[0056] (3)

[0057] Where the matrix A represents the CT scanning system matrix of size , where is the number of X-rays, and is the size equal to the number of pixels of the image after reconstruction, is the CT image of the object to be reconstructed and detected, is the finite-angle CT projection data obtained, is a diagonal matrix, and the values of its diagonal elements are , and are all regularization parameters.

[0058] Specifically, based on the dual-regularized CT reconstruction optimization model (3), two intermediate variables and are introduced to establish an optimization problem with equality constraints as follows:

[0059]

[0060] Using the augmented Lagrangian multiplier method, the Lagrangian multiplier is introduced to convert the above optimization problem with equality constraints (4) into an unconstrained optimization problem as follows:

[0061]

[0062] where and are positive parameters, and are dual variables. The above unconstrained optimization problem (5) is solved using the alternating direction method of multipliers, and the iteration formula is as follows:

[0063]

[0064] To avoid calculating the inverse of the system matrix the gradient descent method is selected to solve the optimization sub-problem (6.1), and we get:

[0065] (7)

[0066] The hard threshold method is used to solve the optimization sub-problem (6.2), and the formula for calculating is as follows:

[0067] (8)

[0068] where ;

[0069] The soft threshold method is used to solve the optimization sub-problem (6.3), and the formula for calculating is as follows:

[0070] (9)

[0071] where soft() is a function that implements the soft threshold operation;

[0072] Finally, when the iteration formula of equation (6) converges, the reconstructed CT image is output.

[0073] The implementation basis of each embodiment of the present invention is achieved through programmed processing by a device with processor functions. Therefore, in engineering practice, the technical solutions and their functions of each embodiment of the present invention are encapsulated into various modules. Based on this actual situation, on the basis of the above embodiments, an embodiment of the present invention provides a limited-angle CT iterative reconstruction system based on tight-frame wavelet transform, which is used to execute a limited-angle CT iterative reconstruction method based on tight-frame wavelet transform in the above method embodiments.

[0074] See Figure 2, the system includes: a data acquisition module for acquiring a pre-image of an object to be detected and limited-angle CT projection data; an initial optimization model construction module for constructing an optimization model based on the pre-image of the object to be detected with total variation regularization constraint; an image optimization module for solving the optimization model to obtain a high-quality pre-CT image, and performing a transform on the high-quality pre-CT image using a tight-frame wavelet transform to obtain tight-frame wavelet frequency-domain coefficients; a double regularization model construction module for establishing a double regularization CT reconstruction optimization model based on the limited-angle CT projection data and the object to be detected before reconstruction, in combination with the tight-frame wavelet transform frequency-domain coefficients; and an image reconstruction module for solving the regularization CT reconstruction optimization model and outputting a CT image of the object to be detected after reconstruction.

[0075] An iterative reconstruction system for limited-angle CT based on tight-frame wavelet transform provided by an embodiment of the present invention adopts Figure 2 several modules therein. By performing total variation regularization constraint on the pre-image, an optimization model is established and a high-quality pre-image is obtained, suppressing the artifacts and noise of the limited-angle CT image, greatly improving the quality of the reconstructed image, and thus improving the clinical diagnosis quality.

[0076] Based on the same inventive concept as the foregoing embodiment, an embodiment of the present invention further provides an electronic device, including a memory and a processor. The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the iterative reconstruction method for limited-angle CT based on tight-frame wavelet transform as proposed in the above embodiment.

[0077] This embodiment also provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it is used to implement the suppression of the CT pre-image, improve the quality of the reconstructed CT image, and protect features such as the structure and edges of the object to be detected. The storage medium may be any non-volatile storage device such as a hard disk, a solid-state drive, a flash drive, an optical disc, etc., for storing computer program code and necessary data files. The stored computer program includes: a data acquisition module, an initial optimization model construction module, an image optimization module, a double regularization model construction module, and an image reconstruction module.

[0078] Finally, it should be noted that the above specific embodiments are only relatively representative examples of the present invention. Obviously, the present invention is not limited to the above specific embodiments and there can be many variations. Any simple modification, equivalent change, and modification made to the above specific embodiments based on the technical essence of the present invention should be considered to fall within the protection scope of the present invention.

Claims

1. A method for iterative reconstruction of limited angle CT based on tight frame wavelet transform, characterized in that: The following steps are involved: Data acquisition, obtaining the pre-image and limited-angle CT projection data of the object to be detected; Initial model optimization: based on the pre-image of the object to be detected, the total variation regularization constraint is performed to build the initial optimization model; Image optimization, solving the initial optimization model to obtain a high-quality pre-CT image, using tight frame wavelet transform to transform the high-quality pre-CT image to obtain tight frame wavelet frequency domain coefficients; A double regularization model is constructed, based on the limited angle CT projection data and the object to be detected before reconstruction, combined with the tight frame wavelet transform frequency domain coefficients, to establish a double regularization CT reconstruction optimization model; Image reconstruction, solving the dual regularized CT reconstruction optimization model, and outputting a reconstructed CT image of the object to be detected based on the solution result.

2. The method for iterative reconstruction of limited angle CT based on tight frame wavelet transform according to claim 1, characterized in that: The data collection specifically includes: An early CT image of the object to be detected is obtained as a pre-image, and limited-angle CT projection data is obtained through limited-angle CT scanning.

3. The method for iterative reconstruction of limited angle CT based on tight frame wavelet transform according to claim 1, characterized in that: The initial optimization of the model is specifically as follows: The total variation regularization constraint is applied to the pre-image of the object to be detected, and the initial optimization model is established as follows: ， in, is the pre-image, is the object to be detected before reconstruction, To solve the high-quality pre-CT images obtained by the optimization model, is a regularization parameter greater than 0, is the total variation regularization constraint.

4. The method for iterative reconstruction of limited angle CT based on tight frame wavelet transform according to claim 1, characterized in that: The image optimization is specifically as follows: The high-quality pre-CT images obtained by solving the optimization model are transformed using tight frame wavelet transform, and the tight frame wavelet frequency domain coefficients are obtained. , the formula is as follows: ， in, is the index of the frequency domain subband, is the tight frame wavelet transform.

5. The method for iterative reconstruction of limited angle CT based on tight frame wavelet transform according to claim 1, characterized in that: The dual regularization model is constructed specifically as follows: Based on the limited-angle CT projection data acquired by data acquisition, the sparse regularization constraints of the object to be detected in the tight frame wavelet frequency domain before reconstruction are designed. ; An L1-based residual regularization term is introduced to transform the frequency domain coefficients of the object to be detected before reconstruction under the tight frame wavelet transform and the frequency domain coefficients of the tight frame wavelet transform. Apply approximation constraints; Combining the sparse characteristics of the tight frame wavelet frequency domain of the object to be detected before reconstruction and the frequency domain coefficients of the tight frame wavelet transform and the tight frame wavelet frequency domain coefficients Similar characteristics, the 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, The size of is equal to the number of pixels in the reconstructed image. is the CT image of the object to be detected before reconstruction, is the acquired limited angle 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 method for iterative reconstruction of limited angle CT based on tight frame wavelet transform according to claim 1, characterized in that: The image reconstruction is specifically as follows: The double regularized CT reconstruction optimization model is solved by using an alternating direction multiplier method, and a reconstructed CT image of the object to be detected is output based on the solution.

7. A limited angle CT reconstruction system based on tight frame wavelet transform, characterized in that: include: A data acquisition module, used to obtain a pre-image and limited-angle CT projection data of the object to be detected; An initial optimization model building module is used to perform total variation regularization constraints based on a pre-image of the object to be detected and build an optimization model; An image optimization module is used to solve the optimization model to obtain a high-quality pre-CT image, and to transform the high-quality pre-CT image using a tight frame wavelet transform to obtain tight frame wavelet frequency domain coefficients; A dual regularization model building module, used to establish a dual regularization CT reconstruction optimization model based on the limited angle CT projection data and the object to be detected before reconstruction, combined with the tight frame wavelet transform frequency domain coefficients; The image reconstruction module is used to solve the regularized CT reconstruction optimization model and output the reconstructed CT image of the object to be detected.

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 limited angle CT reconstruction method based on tight frame wavelet transform according to any one of claims 1 to 6 are implemented.

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

Images