Sparse CT reconstruction method based on complementary prior and implicit neural representation
By introducing complementary prior models and implicit neural representations in CT reconstruction, combining semiquadratic splitting method and alternating optimization strategy, the problem of image quality decline in sparse CT reconstruction is solved, and a more efficient and stable reconstruction effect is achieved.
Patent Information
- Application Number
- CN202411586179.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-08
- Publication Date
- 2025-02-18
AI Technical Summary
In CT imaging, the data loss problem caused by sparse sampling leads to the decline in image quality of traditional reconstruction algorithms, with artifacts and noise challenges, and the existing methods perform poorly under extremely sparse sampling.
The sparse CT reconstruction method based on complementary priors and implicit neural representations is adopted, and the complementary prior models are constructed by decoupling the problem through semiquadratic splitting method, combining the implicit depth image priors and display self-similarity and sparse priors. And embed it in an implicit neural network, balancing data-driven and prior-driven through alternating optimization strategies.
The quality and stability of sparse CT reconstruction images are improved, and the weight of the interval balance sub-problem is refined by hyperparameters to ensure efficient convergence of the optimization process, which is better than many other regularization solutions.
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Figure CN119478096A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of artificial intelligence and biomedical imaging technology, and in particular relates to a sparse CT reconstruction method based on complementary priors and implicit neural representation. Background Art
[0002] Computed tomography, as a common medical imaging technology, has been widely used in clinical diagnosis. However, the radiation generated by X-rays during CT imaging can bring potential health risks to patients. In existing CT imaging, sparse sampling technology is one of the main means to reduce X-ray radiation. However, due to the missing characteristics of sparse measurement data, the use of traditional reconstruction algorithms (such as FBP, SART, etc.) will inevitably lead to a decrease in the quality of reconstructed images. CT images face challenges such as artifacts and noise. Existing regularization-based methods can improve the image reconstruction quality to a certain extent by using prior information, but they still perform poorly under extremely sparse sampling. Therefore, a more efficient method is needed to improve the image quality of sparse CT reconstruction.
[0003] In recent years, self-supervised deep learning methods have made promising progress in CT reconstruction. However, in practical medical imaging applications, the lack of high-quality training sets for use as labels is very challenging. Deep image prior is an unsupervised method that shows that neural networks inherently have low impedance to natural signals and high impedance to noise. DIP does not require a training set, and only a single sparsely sampled sinusoidal image is needed to achieve CT reconstruction tasks. DIP provides a new method for regularization of inverse problems, but the use of a single deep image prior still needs to be improved in terms of imaging quality and speed.
[0004] Existing neural implicit representation techniques have shown some potential in CT reconstruction, but their unsupervised nature leads to insufficient constraints in the solution space, especially in highly pathological reconstruction tasks;
[0005] To overcome these challenges, the present invention proposes a neural representation method combining a complementary prior model that can enhance the feasibility of the solution space and improve the stability and accuracy of reconstruction. Summary of the invention
[0006] The purpose of the present invention is to provide a sparse CT reconstruction method based on complementary prior and implicit neural representation, which can effectively combine prior knowledge by embedding the complementary prior model into the network structure of implicit neural representation, and reconstruct the target CT image through implicit neural representation learning.
[0007] The technical solution adopted by the present invention is as follows:
[0008] A sparse CT reconstruction method based on complementary priors and implicit neural representations, incl.
[0009] S1: The semi-quadratic splitting method is used to decouple the sparse CT reconstruction problem into a data term subproblem driven by the physical model and a prior term subproblem driven by data priors.
[0010] S2: The implicit deep image prior and explicit prior knowledge such as self-similarity and sparsity are combined through the denoising regularization method to construct a complementary prior model to solve the prior term sub-problem;
[0011] S3: The constructed complementary prior model is embedded into the network structure of the implicit neural network, and the data item sub-problem is solved by using implicit neural representation learning with prior embedding;
[0012] S4: Based on the semi-quadratic splitting method, the alternating optimization strategy is improved to interleave the solution of the data fidelity subproblem with the solution of the distribution prior subproblem, so as to balance the data-driven and prior-driven aspects in the reconstruction process.
[0013] In some embodiments, the forward sampling model of the sparse CT reconstruction in S1 can be expressed as the following mathematical formula:
[0014] y=Ax+n#(1)
[0015] First, under the sparse sampling mechanism setting, the image is solved in the measurement value y, which can be expressed as follows:
[0016]
[0017] The semi-quadratic splitting method is used to separate variables, an auxiliary variable z is introduced, and it is converted into a constrained optimization problem:
[0018]
[0019] Then, according to the Lagrange multiplier method, the constraint z=x is incorporated into the objective function to construct the Lagrangian function:
[0020]
[0021] By alternately optimizing the two variables x and z, the original problem is optimized into two sub-problems:
[0022]
[0023] In some embodiments, the following formula is used as a regularization function for denoising regularization in S2:
[0024]
[0025] By extending the regularization of the deep image prior through denoising regularization, equation (5b) can be transformed into the following objective function:
[0026]
[0027] The alternating direction multiplier method (ADMM) is used to solve equation (7). First, the constraint term is converted into a penalty term using augmented Lagrangian:
[0028]
[0029] Combining the last two terms of (8), we obtain:
[0030]
[0031] The ADMM algorithm is equivalent to the three unknown quantities in this expression: θ, z k and u k Perform sequential updates, fix z k and u k Update θ by solving the following equation:
[0032]
[0033] Fixed θ and u k , update z k :
[0034]
[0035] Using the fixed-point strategy, the above relative to z k The reciprocal of is set to zero, and the Derive the update formula:
[0036]
[0037] Fixed θ and z k , update u k :
[0038] u k+1 =u k -z k +G θ #(13)
[0039] In some embodiments, the step of embedding the constructed complementary prior model into the network structure of the implicit neural network in S3, and solving the data item sub-problem by using implicit neural representation learning with prior embedding, specifically comprises the following steps:
[0040] S3-1: The underlying CT image is modeled as an implicit continuous function that maps image coordinates to intensities;
[0041] S3-2: Perform CT imaging forward modeling to simulate the physical acquisition process from images to their corresponding projection measurements;
[0042] S3-3: Optimize an MLP network to approximate the implicit function by minimizing the error in the measurement domain;
[0043] S3-4: The prior image obtained by solving the complementary prior model is refined and embedded into the multi-layer perceptron network structure of implicit neural representation to complete the overall process, thereby improving the stability and accuracy of the solution.
[0044] In some embodiments, the step S3-4 incorporates the generative prior in the complementary prior model into the implicit neural representation model, specifically by integrating the prior image z k Expressed as a continuous function of image coordinates, it can be expressed as follows:
[0045]
[0046] Using a multi-layer perceptron network F Θ The function f is approximated by optimizing the following objective function:
[0047]
[0048] In some embodiments, the specific steps of refining the prior image in S3-4 are:
[0049] S3-4-1: Refine the data items after embedding the prior image and integrate the CT imaging model to improve the MLP network F Θ ;
[0050] S3-4-2: Data items are defined as
[0051]
[0052] The optimization of the image space is transformed into the optimization of the MLP parameter space;
[0053] S3-4-3: Convert the optimization in image space into the optimization in MLP parameter space;
[0054] S3-4-4: Initialize Θ through the prior image, encode the prior information into the structure of the network, and then use the implicit neural network representation to learn the distribution of the measured value y to further optimize F Θ
[0055]
[0056] After data fidelity refinement is completed, the MLP network represents a solution of the kth iteration of the semi-quadratic splitting method, which inherits the generative prior z in the complementary prior modelk , which is also highly consistent with the actual measured value y. Then, the necessary image coordinates p are input into the MLP network. The reconstructed image of the kth iteration of the semi-quadratic splitting method is obtained, that is,
[0057] The technical effects achieved by the present invention are:
[0058] 1. By introducing the hyperparameter refinement interval (RI) to balance the weights of the two sub-problems in the overall process, RI enables the data fidelity sub-problem to be executed at a specified time step, thereby efficiently optimizing between the two sub-problems of data fidelity and distribution prior, ensuring that the inverse problem is gradually converged to the optimal solution;
[0059] 2. The complementary prior model can use existing advanced denoisers as prior information while extending the DIP prior information, and outperforms many other regularization schemes. The alternating optimization strategy can clearly distinguish between the data-driven and prior-driven aspects of the reconstruction problem, further improving the quality of the reconstructed image. BRIEF DESCRIPTION OF THE DRAWINGS
[0060] Figure 1 It is a schematic diagram of the sparse projection data processing flow method of the present invention;
[0061] Figure 2 It is a specific schematic diagram of the process of using the semi-quadratic splitting method of the present invention;
[0062] Figure 3 It is a schematic diagram of a specific process of obtaining a denoised image by the denoiser of the present invention;
[0063] Figure 4 It is a schematic diagram of the a priori image processing method of the present invention. DETAILED DESCRIPTION
[0064] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is specifically described below in conjunction with embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present invention, and does not strictly limit the scope of protection of the specific claims of the present invention.
[0065] Example:
[0066] like Figure 1 As shown, a sparse CT reconstruction method based on complementary prior and implicit neural representation includes:
[0067] S1: The semi-quadratic splitting method is used to decouple the sparse CT reconstruction problem into a data term subproblem driven by the physical model and a prior term subproblem driven by data priors.
[0068] S2: The implicit deep image prior and explicit prior knowledge such as self-similarity and sparsity are combined through the denoising regularization method to construct a complementary prior model to solve the prior term sub-problem;
[0069] S3: The constructed complementary prior model is embedded into the network structure of the implicit neural network, and the data item sub-problem is solved by using implicit neural representation learning with prior embedding;
[0070] S4: Based on the semi-quadratic splitting method, the alternating optimization strategy is improved to interleave the solution of the data fidelity subproblem with the solution of the distribution prior subproblem, so as to balance the data-driven and prior-driven aspects in the reconstruction process.
[0071] like Figure 1-4 As shown, the forward sampling model of sparse CT reconstruction in S1 can be expressed as the following mathematical formula:
[0072] y=Ax+n#(1)
[0073] Sparse projection data is generated from a two-dimensional clean CT image by Radon transform, and Gaussian noise is added to generate noisy projections. The resolution of all test images is fixed to 512x512 pixels. 64 uniformly distributed projections are generated in the range of 0 to 180 degrees. The vector y is the measurement data, A is the forward model of CT imaging, such as Radon transform, x is the vector form of the required potential CT image, and n is the system noise. This example seeks to reconstruct the unknown CT image x from the observed measurement value y;
[0074] Under the sparse acquisition mechanism, the dimension of the measurement value y is often much lower than the dimension of the image x, which makes the CT reconstruction task highly ill-posed. Therefore, a general solution is to solve the optimization problem by adding appropriate regularization to x. First, under the sparse sampling mechanism setting, the image is solved in the measurement value, which can be expressed as follows:
[0075]
[0076] Where x represents the CT image to be solved. represents the data fidelity term, which is used to measure the similarity between the true measurement y and the estimated measurement Ax. is a regularization term that constrains the solution space by imposing prior knowledge, and λ>0 is a hyperparameter that controls the contribution of the regularization term;
[0077] In order to solve problem (2) more efficiently, this solution first uses a variable separation method to decouple the data term and the prior term. The semi-quadratic splitting method is used to separate the variables, an auxiliary variable z is introduced, and the problem is converted into a constrained optimization problem:
[0078]
[0079] Then, according to the Lagrange multiplier method, the constraint z=x is incorporated into the objective function to construct the Lagrangian function:
[0080]
[0081] By alternating optimization and two variables, the original problem is optimized into two sub-problems:
[0082]
[0083] where μ is a penalty parameter, σ 2 is the variance of the observation noise. By alternately optimizing the two variables x and z, the original problem can be decomposed into two simpler sub-problems, where equation (5a) is the data term sub-problem, focusing on identifying k-1 The related neighboring points control the distance between the measured projection and the estimated projection; Formula (5a) is a priori sub-problem. From the perspective of Bayesian analysis, it can be regarded as a Gaussian denoising problem. The priori sub-problem is further rewritten into a Gaussian denoising form, and the existing denoising operator can be used to play the role of image prior;
[0084] In this embodiment, it can be found that Figure 1 This is a structural diagram of the complementary prior model driving implicit neural representation learning. This embodiment uses an efficient complementary prior model to solve the prior term subproblem, and uses the implicit neural representation driven by the complementary prior to solve the data term subproblem. Then, based on the semi-quadratic splitting (HQS) framework, a hyperparameter refinement interval (RI∈R) is introduced to balance the weights of the two subproblems in the overall process. RI allows the data fidelity subproblem to be executed at a specified time step ((k-1)mod RI≠0).
[0085] like Figure 1-4 As shown, the following formula is used in S2 as the regularization function for denoising regularization:
[0086]
[0087] According to the process Figure 2 As shown in Figure 2, a complementary prior model based on deep image prior is used to solve the prior subproblem in the HQS framework. The construction principle of the complementary prior model is to add an explicit prior to the implicit deep image prior, thereby enriching the overall regularization effect. Denoising regularization is a popular technique for constructing a denoising algorithm into a regularization. It can accommodate additional regularization steps in the deep image prior framework.
[0088] Where f(·) is an optional denoiser. By extending the regularisation of the deep image prior through denoising regularisation, (5b) can be transformed into the following objective function:
[0089]
[0090] Among them G θ is a convolutional neural network parameterized by θ, and γ is a regularization parameter used to balance the implicit regularization of DIP and the explicit regularization of RED. The alternating direction multiplier method is used to solve equation (7). First, the constraint term is converted into a penalty term using augmented Lagrangian:
[0091]
[0092] where u k represents the Lagrange multiplier vector of the set of equality constraints, v is an optional free parameter, and combining the last two terms of (8), we obtain:
[0093]
[0094] The alternating direction multiplication method is equivalent to the three unknown quantities in this expression: θ, z k and u k Perform sequential updates, fix z k and u k Update θ by solving the following equation:
[0095]
[0096] Fixed θ and u k , update z k :
[0097]
[0098] This is a classic RED target, representing the image G θ +u k One option to solve this problem is to adopt a fixed-point strategy and convert the above k The reciprocal of is set to zero, and the Derive the update formula, where j is z k Updated internal iteration count:
[0099]
[0100] Fixed θ and z k , update u k :
[0101] u k+1 =u k -z k +Gθ #(13)
[0102] In this embodiment, by adjusting θ, z k and u k The prior subproblem is solved by sequential updates. In the process of loop iteration, the most time-consuming is the update of θ. In order to save running time, we apply the denoiser once every few outer iterations of ADMM and run the denoiser and θ updates in parallel, as shown in Figure 3 shown.
[0103] like Figure 1-4 As shown, the constructed complementary prior model in S3 is embedded into the network structure of the implicit neural network, and the data item sub-problem is solved by using implicit neural representation learning with prior embedding. The specific steps are:
[0104] S3-1: The underlying CT image is modeled as an implicit continuous function that maps image coordinates to intensities;
[0105] S3-2: Perform CT imaging forward modeling to simulate the physical acquisition process from images to their corresponding projection measurements;
[0106] S3-3: Optimize an MLP network to approximate the implicit function by minimizing the error in the measurement domain;
[0107] S3-4: Refine the prior image obtained by solving the complementary prior model and embed it into the multi-layer perceptron network structure of implicit neural representation to complete the overall process.
[0108] In this embodiment, Figure 4 The proposed method is a flowchart of implicit neural representation with prior embedding. By embedding the prior image obtained by solving the complementary prior model into the multi-layer perceptron (MLP) network structure of implicit neural representation, the feasibility of the solution space of the inverse problem is effectively increased, thereby improving the stability and accuracy of the solution.
[0109] like Figure 1-4 As shown, the generative prior in the complementary prior model is integrated into the implicit neural representation model in S3-4, specifically, the prior image z k Expressed as a continuous function of image coordinates, it can be expressed as follows:
[0110]
[0111] Using a multi-layer perceptron network F Θ The function f is approximated by optimizing the following objective function:
[0112]
[0113] In this embodiment, the goal at this stage is to convert the generative prior z in the complementary prior model into k Incorporated into the implicit neural representation model, this strategy prevents INR from generating degenerate reconstruction solutions by avoiding overfitting to incomplete measurements y. Technically, the prior image z k It is expressed as a continuous function of image coordinates, where p is an arbitrary spatial coordinate, z k (p) is the corresponding intensity of the prior image at that position. We use the multi-layer perceptron (MLP) network F Θ The function f is approximated by optimizing the following objective function, where N represents the number of sampled image coordinates at each iteration, and p i Represents the i-th spatial coordinate. After the optimization is completed, the prior image z k (p) Embedded in the trainable weight Θ prior of the MLP network, from the perspective of initialization, the generative prior provided by the complementary prior model is used to construct a feasible initialization for the INR model that follows the target distribution.
[0114] like Figure 1-4 As shown, the specific steps of refining the prior image in S3-4 are:
[0115] S3-4-1: Refine the data items after embedding the prior image and integrate the CT imaging model to improve the MLP network F Θ ;
[0116] S3-4-2: Data items are defined as
[0117]
[0118] After prior embedding, the INR network F Θ The prior is fused with the prior image z k , since the prior image is generated from random sampling, it lacks data fidelity to the real incomplete measurement y. Therefore, we need to improve the MLP network F by integrating the CT imaging model Θ .
[0119] The optimization of the image space is transformed into the optimization of the MLP parameter space;
[0120] S3-4-3: Convert the optimization in image space into the optimization in MLP parameter space;
[0121] S3-4-4: Initialize Θ through the prior image, encode the prior information into the structure of the network, and then use the implicit neural network representation to learn the distribution of the measured value y to further optimize F Θ
[0122]
[0123] After data fidelity refinement is completed, the MLP network represents a solution of the kth iteration of the semi-quadratic splitting method, which inherits the generative prior z in the complementary prior model k , which is also highly consistent with the actual measured value y. Then, the necessary image coordinates p are input into the MLP network. The reconstructed image of the kth iteration of the semi-quadratic splitting method is obtained, that is,
[0124] The above is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. The structures, devices and operating methods not specifically described and explained in the present invention are implemented according to conventional means in the art unless otherwise specified and limited.
Claims
1. A sparse CT reconstruction method based on complementary priors and implicit neural representation, characterized in that: include: S1: The semi-quadratic splitting method is used to decouple the sparse CT reconstruction problem into a data term subproblem driven by the physical model and a prior term subproblem driven by data priors. S2: The implicit deep image prior and the explicit self-similarity and sparsity prior knowledge are combined through the denoising regularization method to construct a complementary prior model to solve the prior term sub-problem; S3: The constructed complementary prior model is embedded into the network structure of the implicit neural network, and the data item sub-problem is solved by using implicit neural representation learning with prior embedding; S4: Based on the semi-quadratic splitting method, the alternating optimization strategy is improved to interleave the solution of the data fidelity subproblem with the solution of the distribution prior subproblem, so as to balance the data-driven and prior-driven aspects in the reconstruction process.
2. The sparse CT reconstruction method based on complementary prior and implicit neural representation according to claim 1, characterized in that: The forward sampling model of sparse CT reconstruction in S1 can be expressed as the following mathematical formula: y=Ax+n#(1) First, under the sparse sampling mechanism setting, the image is solved in the measurement value y, which can be expressed as follows: The semi-quadratic splitting method is used to separate variables, an auxiliary variable z is introduced, and it is converted into a constrained optimization problem: Referring to the Lagrange multiplier method, the constraint z=x is incorporated into the objective function to construct the Lagrange function: By alternately optimizing the two variables x and z, the original problem is optimized into two sub-problems:
3. The sparse CT reconstruction method based on complementary prior and implicit neural representation according to claim 2, characterized in that: The following formula is used as the regularization function for denoising regularization in S2: By extending the regularization of the deep image prior through denoising regularization, equation (5b) can be transformed into the following objective function: The alternating direction multiplier method is used to solve equation (7). First, the constraint term is converted into a penalty term using augmented Lagrangian: Combining the last two terms of (8), we obtain: The ADMM algorithm is equivalent to the three unknown quantities in this expression: θ, z k and u k Perform sequential updates to fix z k and u k and θ are updated by solving (9) and (8) as follows: Fixed θ and u k , update z k : Relative to z k The reciprocal of is set to zero, and the Derive the update formula: Fixed θ and z k , update u k : u k+1 =u k -z k +G θ #(13) 4. The sparse CT reconstruction method based on complementary prior and implicit neural representation according to claim 3, characterized in that: The sparse CT reconstruction problem in S3 is decoupled into a data term sub-problem driven by a physical model and a prior term sub-problem driven by data priors. The specific steps are: S3-1: The underlying CT image is modeled as an implicit continuous function that maps image coordinates to intensities; S3-2: Perform CT imaging forward modeling to simulate the physical acquisition process from images to their corresponding projection measurements; S3-3: Optimize an MLP network to approximate the implicit function by minimizing the error in the measurement domain; S3-4: Refine the prior image obtained by solving the complementary prior model and embed it into the multi-layer perceptron network structure of implicit neural representation to complete the overall process.
5. The sparse CT reconstruction method based on complementary prior and implicit neural representation according to claim 4, characterized in that: The S3-4 integrates the generative prior in the complementary prior model into the implicit neural representation model, specifically by converting the prior image z k Expressed as a continuous function of image coordinates, it can be expressed as follows: Using a multi-layer perceptron network F Θ The function f is approximated by optimizing the following objective function:
6. The sparse CT reconstruction method based on complementary prior and implicit neural representation according to claim 5, characterized in that: The specific steps of refining the prior image in S3-4 are: S3-4-1: Refine the data items after embedding the prior image and integrate the CT imaging model to improve the MLP network F Θ ; S3-4-2: Data items are defined as The optimization of the image space is transformed into the optimization of the MLP parameter space; S3-4-3: Convert the optimization in image space into the optimization in MLP parameter space; S3-4-3: Initialize Θ through the prior image, encode the prior information into the structure of the network, and then use the implicit neural network representation to learn the distribution of the measured value y to further optimize F Θ 7. The data item refinement training method according to claim 6, characterized in that: After data fidelity refinement is completed, the MLP network represents a solution of the kth iteration of the semi-quadratic splitting method, which inherits the generative prior z in the complementary prior model k , which is also highly consistent with the actual measured value y, and the necessary image coordinates p are input into the MLP network The reconstructed image of the kth iteration of the semi-quadratic splitting method is obtained, that is,