Fault enhancement reconstruction method based on composite regular optimization model
By combining a composite regularization optimization model and weight correction, along with anisotropic total variation and curvilinear sparsity regularization terms, the noise and artifact problems in tomographic reconstruction are solved, achieving efficient and accurate image reconstruction results.
Patent Information
- Application Number
- CN202511910651.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-17
- Publication Date
- 2026-03-20
AI Technical Summary
In existing tomographic reconstruction techniques, the reconstructed images suffer from severe noise, edge artifacts, and poor representation of fine structures such as curves due to low signal-to-noise ratio of projection data, incomplete data, and limited detector effects.
A composite regularized optimization model is adopted, which combines anisotropic total variation and curvelet sparsity regularization terms. The model is solved iteratively by the primal-dual hybrid gradient algorithm to construct the optimization model and perform weight correction to compensate for the finite detector effect, suppress noise and maintain the fine structure of the image.
It achieves accurate modeling of multi-scale and multi-directional geometric features of complex images, significantly suppresses edge artifacts in reconstructed images, improves reconstruction quality while maintaining image clarity, and has high computational efficiency and stability.
Smart Images
Figure CN121708158A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of tomographic imaging reconstruction technology, and specifically to a tomographic enhancement and reconstruction method based on a composite regularized optimization model. Background Technology
[0002] Tomographic imaging technology reconstructs the internal three-dimensional structure of an object by acquiring projection data from multiple angles and using mathematical algorithms. It has wide applications in medical imaging, materials science, and biology. However, in many practical applications, the quality of the acquired projection data is far from ideal. For example, in cryo-electron computed tomography (cryo-electron computed tomography), extremely low electron doses must be used to avoid radiation damage to biological samples from high-energy electron beams, resulting in a very low signal-to-noise ratio in the projection data. Simultaneously, due to physical limitations, the tilt angle of the sample stage is limited, causing incomplete projection data (i.e., the "missing wedge" problem). These factors collectively lead to traditional reconstruction algorithms, such as filtered backprojection, producing results riddled with noise and artifacts.
[0003] To overcome these challenges, iterative reconstruction algorithms based on variational regularization models have become an important research direction. This method transforms the reconstruction problem into an optimization problem of minimizing an energy functional, constraining the solution space by introducing regularization terms that reflect prior knowledge of the image. Total variational regularization is a classic regularization term that assumes the image is piecewise constant, and it is effective in suppressing noise and preserving large-scale edges of objects. However, total variational regularization tends to turn smooth transition regions in the image into piecewise constants as well, producing a "staircase effect" that compromises the realism of fine structures.
[0004] Furthermore, the "finite detector" problem is prevalent in practical tomographic scanning systems. This means the physical size of the detector is insufficient to cover the complete projection of the object at all angles, resulting in truncated projection data. When reconstruction algorithms fit this truncated projection data to a model that does not include objects outside the field of view, artifacts appear at the edges of the reconstructed volume, severely impacting reconstruction quality and subsequent analysis. Existing methods for addressing this problem, such as expanding the reconstruction volume to simultaneously reconstruct objects inside and outside the field of view, drastically increase computational load and memory consumption.
[0005] Therefore, there is an urgent need in this field for a new reconstruction method that can not only effectively handle the problems of low signal-to-noise ratio and data incompleteness, but also accurately model and preserve multi-scale, anisotropic features (such as curves and textures) in the image, while being able to correct artifacts introduced by finite detector effects in a computationally efficient manner. Summary of the Invention
[0006] The purpose of this invention is to provide a tomographic enhancement and reconstruction method based on a composite regular optimization model, which aims to solve the technical problems in existing tomographic imaging reconstruction technology, such as severe noise, edge artifacts, and poor representation of fine structures such as curves, caused by low signal-to-noise ratio of projection data, incomplete data, and limited detector effects.
[0007] To solve the above-mentioned technical problems, the specific technical solution adopted by the present invention is as follows: A composite regularized tomographic image reconstruction method, comprising the following steps: S1: Obtain the original tilt sequence projection data ; and the projection data Perform weight correction to generate preprocessed projection data. To compensate for the limited detector effect; S2: Construct an optimization model based on weighted data fidelity terms and composite regularization terms; the optimization model is as follows: ; in, Represents the discrete projection operator. Represents the volumetric data of the three-dimensional image to be solved; For weighted data fidelity items, It is a diagonal weighted matrix, and the fidelity term is used to measure the weighted least squares error between the projection of the reconstruction result and the preprocessed projection data; This is the total variational regularization term for anisotropy, used to promote smooth image segmentation and maintain clear structural boundaries; For the curvilinear sparsity regularization term, where For the curvelet transform operator, this term utilizes the sparsity of features such as curves and edges in the image in the curvelet domain for constraint; and , which are positive constants, are regularization parameters that control the strength of the total variational regularization term for anisotropy and the curvilinear sparsity regularization term, respectively; S3: The primal-dual hybrid gradient algorithm (PDHG) is used to iteratively solve the optimization model constructed in S2. The solution process continues until the maximum number of iterations is reached, and the reconstructed 3D image volume data is output. .
[0008] Furthermore, in S1, weight correction is performed on the original projection data using a pre-calculated correction factor. This is achieved through pixel-by-pixel multiplication. The correction factor is determined based on the geometry of the tomographic scan and is used to compensate for the contribution of objects outside the reconstructed field of view to the acquired projection data. Specifically, due to the actual acquired projection data... It contains full-thickness integral information of the real sample, while Only the voxel contribution within the reconstructed field of view is considered, and the residual is calculated directly. This can lead to severe truncation artifacts and cupping effects in the reconstructed volume. To establish a physically consistent measure, this invention constructs a residual term. , where the matrix This is a theoretical diagonal weighted matrix corresponding to the geometry of the entire sample during data acquisition. The values of its diagonal elements are determined based on the analytically estimated path length of the ray passing through the entire sample, including both the reconstructed field of view and the out-of-field region. This can be derived... Therefore, the preprocessed projection data after long object compensation can be obtained as follows: .
[0009] Furthermore, in S2, the curvelet sparsity regularization term utilizes the multi-scale, multi-directional, and anisotropic properties of the curvelet transform to apply the sparsity regularization term to conditions with… The curvilinear features of smooth singularities provide optimal sparse representations, thereby accurately preserving the fine structure of the image while suppressing noise.
[0010] Furthermore, in S3, the PDHG algorithm framework is suitable for solving optimization problems consisting of the sum of multiple (especially non-smooth) sub-terms, and can decompose complex global problems into a series of sub-problems with efficient solutions. The process of solving the problem using the primal-dual hybrid gradient algorithm includes: initializing the primal variables and the corresponding dual variables, and then alternately executing the update steps of the dual variables and the update steps of the primal variables; wherein, the update step of each variable is decomposed into a subtask with a closed solution or a simple proximal operator, the proximal operator including a soft thresholding operation for the anisotropic total variational term and the curvelet sparsity term.
[0011] Furthermore, the S3 iterative solution process is specifically as follows: First, set the initial 3D image. and dual variables Here, all vectors are set to zero; then the main iteration loop begins: S3-1: Dual Variable Update: Parallel update of the three dual variables associated with the data fidelity term, the anisotropic total variation term, and the curvilinear term; the specific update formula is as follows: ; ; ; in, The soft threshold operator is defined as follows: , This is the step size parameter; S3-2: Update original variables: Update the 3D image It has a simple closed-form solution:
[0012] in, and These are the gradient operator and the adjoint operator of the curvelet transform, respectively. This is the step size parameter; S3-3: Extrapolation step: Extrapolation is performed after each iteration to improve the convergence speed.
[0013] in, These are extrapolated parameters; S3-4: Convergence check: Check if the maximum number of iterations has been reached; if so, end the iteration; otherwise, return to the dual variable update step.
[0014] Compared with the prior art, the present invention has the following beneficial effects:
[0015] (1) Precise Image Prior Modeling: For the first time, an anisotropic total variation and curvelet sparsity are combined to construct a composite regularization model. The anisotropic total variation effectively preserves the clear boundaries of large-scale structures, while the curvelet sparsity prior can optimally sparsely represent curves, edges, etc. in the image. Smooth singularity features. The two work together to achieve comprehensive and accurate modeling of multi-scale and multi-directional geometric features of complex images, avoiding the staircase effect caused by a single regularization term.
[0016] (2) Efficient finite detector artifact correction: By introducing a weight correction preprocessing step with extremely low computational cost outside the iterative framework, the projection data mismatch caused by objects outside the field of view is effectively compensated, thereby significantly suppressing the intensity distortion and artifacts of the reconstructed image edges, and without expanding the reconstruction volume, ensuring the applicability of the algorithm to large-scale problems.
[0017] (3) Efficient and stable numerical solution: The entire reconstruction framework is constructed as a separable convex optimization problem and solved using a primal-dual hybrid gradient algorithm. This algorithm decomposes the complex optimization problem into a series of subtasks with closed-form solutions or simple proximal operators (such as soft thresholding), avoiding any complex inner loops or matrix inversions, thus ensuring the computational efficiency and numerical stability of the algorithm, enabling it to efficiently handle large-scale three-dimensional tomographic reconstruction tasks. Attached Figure Description
[0018] Figure 1 The overall flowchart of the algorithm of this invention.
[0019] Figure 2 A schematic diagram of the finite detector problem and weight correction mechanism.
[0020] Figure 3The reconstruction result XY plane slice in Example 2. Detailed Implementation
[0021] The technical solution of the present invention will now be clearly and completely described in conjunction with the accompanying drawings.
[0022] Example 1
[0023] This embodiment uses cryo-electron computed tomography (cryo-electron computed tomography) as an example to explain in detail the implementation process of a tomographic image reconstruction method (the overall process is as follows). Figure 1 (As shown).
[0024] S1: Data acquisition and weight correction.
[0025] First, obtain the aligned tilted sequence projection data of the sample to be reconstructed. Subsequently, weight correction was performed to address the limited detector problem. For example... Figure 2 As shown, the actual acquired projection includes signals from both objects inside and outside the reconstructed field of view (FOV), while the forward projection operator in the iterative algorithm... Simulating only the signal within the FOV results in artifacts due to this mismatch. The weighting correction step involves pre-compiling a correction factor matrix and applying it to the original projection data. Multiply to obtain the preprocessed projection data. This operation aims to eliminate or reduce the contribution of objects outside the field of view, making... Can be better modeled As described.
[0026] S2: Construct a composite regularized optimization model.
[0027] Based on preprocessed projection data The optimization model is constructed as follows: ; The data fidelity term uses a weighted least squares form derived from the SIRT algorithm, with the weighting matrix... The diagonal elements.
[0028] Projection matrix The The reciprocal of the sum of the rows, i.e. Its function is to normalize each projected ray, ensuring that rays passing through thicker regions of the object have equal weight in the optimization process as those passing through thinner regions. This prevents the model from being dominated by a few rays with large contributions, thus enhancing the convergence stability of the algorithm. The composite regularization term combines anisotropic total variation and curvelet sparsity, and its parameters are adjusted... and To balance the protection of piecewise smooth regions and curve features, and The specific value depends on the specific data.
[0029] S3: Iterative solution is performed using a hybrid primal-dual gradient algorithm.
[0030] This step is the core computational component of this method. The algorithm first sets up the initial 3D image. and dual variables Here, all are set to zero vectors. Then, the main iteration loop begins:
[0031] 1. Dual Variable Update: Parallel update of the three dual variables associated with the data fidelity term, the anisotropic total variation term, and the curvelet term. The specific update formula is as follows: ; ; ; in, The soft threshold operator is defined as follows: , This is the step size parameter, which is set to 0.1 here.
[0032] 2. Original variable update: Update the 3D image This step also has a simple closed-form solution.
[0033]
[0034] in, and These are the gradient operator and the adjoint operator of the curvelet transform, respectively. This is the step size parameter, which is set to 0.01 here.
[0035] 3. Extrapolation step: After each iteration, extrapolation is performed to improve the convergence speed.
[0036]
[0037] in, This is an extrapolation parameter, and we take the commonly used value of 1 here.
[0038] 4. Convergence Check: Check if the maximum number of iterations has been reached. If so, end the iteration; otherwise, return to the dual variable update step. Here, the maximum number of iterations is set to 100.
[0039] Example 2
[0040] This embodiment is based on Embodiment 1 and conducts specific experimental verification. The verification datasets selected are EMPIAR 10643 and EMPIAR 10499. For the EMPIAR 10643 dataset, the following data is used: For the EMPIAR 10499 dataset, take... ; Figure 3 The XY plane slices reconstructed from these two datasets using the WBP algorithm, the SIRT algorithm (10 iterations) in IMOD software, and the algorithm of this invention are shown.
[0041] from Figure 3 It can be seen that the reconstruction results obtained by using the algorithm of this invention significantly suppress noise and improve contrast compared with the WBP algorithm and the SIRT algorithm.
[0042] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A composite regularized tomographic image reconstruction method, characterized in that, The method includes the following steps: S1: Obtain the original tilt sequence projection data ; and the projection data Perform weight correction to generate preprocessed projection data. ; S2: Construct an optimization model based on weighted data fidelity terms and composite regularization terms; the optimization model is as follows: ； in, Represents the discrete projection operator. Represents the volumetric data of the three-dimensional image to be solved; For weighted data fidelity items, It is a diagonal weighted matrix, and the fidelity term is used to measure the weighted least squares error between the projection of the reconstruction result and the preprocessed projection data; This is the total variational regularization term for anisotropy, used to promote smooth image segmentation and maintain clear structural boundaries; For the curvilinear sparsity regularization term, where For the curvelet transform operator, this term utilizes the sparsity of features such as curves and edges in the image in the curvelet domain for constraint; and , which are positive constants, are regularization parameters that control the strength of the total variational regularization term for anisotropy and the curvilinear sparsity regularization term, respectively; S3: The primal-dual hybrid gradient algorithm is used to iteratively solve the optimization model constructed in S2. The solution process continues until the maximum number of iterations is reached, and the reconstructed 3D image volume data is output. .
2. The tomographic image reconstruction method as described in claim 1, characterized in that, In step S1, weight correction is performed on the original projection data using a pre-calculated correction factor. This is achieved through pixel-by-pixel multiplication. The correction factor is determined based on the geometry of the tomographic scan and is used to compensate for the contribution of objects outside the reconstructed field of view to the acquired projection data. To establish a physically consistent measure, a residual term is constructed. , where the matrix It is a theoretical diagonal weighted matrix corresponding to the geometry of the entire sample during data acquisition. The values of its diagonal elements are determined based on the analytically estimated path length of the ray passing through the entire sample, including the reconstructed field of view and the region outside the field of view; it can be derived to... Therefore, the preprocessed projection data after long object compensation can be obtained as follows: .
3. The tomographic image reconstruction method as described in claim 1, characterized in that, In S2, the curvelet sparsity regularization term utilizes the multi-scale, multi-directional, and anisotropic properties of the curvelet transform to apply the sparsity regularization term to conditions with... The curvilinear features of smooth singularities provide optimal sparse representations, thereby accurately preserving the fine structure of the image while suppressing noise.
4. The tomographic image reconstruction method as described in claim 1, characterized in that, In S3, the framework of the PDHG algorithm is suitable for solving optimization problems consisting of the sum of multiple sub-items, and can decompose complex global problems into a series of sub-problems with efficient solutions. The process of solving the problem using the primal-dual hybrid gradient algorithm includes: initializing the primal variables and the corresponding dual variables, and then alternately executing the update steps of the dual variables and the update steps of the primal variables; wherein, the update step of each variable is decomposed into a subtask with a closed solution or a simple proximal operator, the proximal operator including a soft thresholding operation for the anisotropic total variational term and the curvilinear sparsity term.
5. The tomographic image reconstruction method as described in claim 4, characterized in that, The S3 iterative solution process is as follows: First, set the initial 3D image. and dual variables Then the main iteration loop begins: S3-1: Dual Variable Update: Parallel update of the three dual variables associated with the data fidelity term, the anisotropic total variation term, and the curvilinear term; the specific update formula is as follows: in, The soft threshold operator is defined as follows: , This is the step size parameter; S3-2: Update original variables: Update the 3D image It has a simple closed-form solution: in, and These are the gradient operator and the adjoint operator of the curvelet transform, respectively. This is the step size parameter; S3-3: Extrapolation step: Extrapolation is performed after each iteration to improve the convergence speed. in, These are extrapolated parameters; S3-4: Convergence check: Check if the maximum number of iterations has been reached; if so, end the iteration; otherwise, return to the dual variable update step.