A method and related equipment for sparse reconstruction of spectral CT by fusing subspace representation and fractional generation model
By fusing subspace representation and fractional generation model, the problems of insufficient photon quantity and severe artifacts in photon-counting spectral CT imaging are solved, achieving efficient and high-quality image reconstruction and improving signal-to-noise ratio and image quality.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Chinese People's Liberation Army Cyberspace Force Information Engineering University
- Filing Date
- 2025-02-14
- Publication Date
- 2026-07-31
AI Technical Summary
Existing technologies in photon-counting spectral CT imaging suffer from problems such as insufficient photon count, severe artifacts, increased noise, and reduced signal-to-noise ratio. Furthermore, deep learning methods rely on high signal-to-noise ratio labeled data, making it difficult to effectively reconstruct high-quality images.
A method combining subspace representation and fraction generation model is adopted. Feature images and orthogonal basis are obtained through subspace recognition. Image denoising is performed by combining block matching and three-dimensional filtering algorithms. High-quality reconstructed images are generated using the trained fraction generation model, and the objective function is optimized to improve the reconstruction effect.
It effectively characterizes the global correlation and detailed texture of energy spectrum CT images, improves image reconstruction quality, reduces artifacts, increases signal-to-noise ratio, and achieves efficient sparse reconstruction.
Smart Images
Figure CN122492890A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of spectral CT reconstruction technology, and in particular to a spectral CT sparse reconstruction method and related equipment that integrates subspace representation and fractional generation model. Background Technology
[0002] Spectral computed tomography (CT) obtains rich information about the internal structure and composition of an object by leveraging the differences in energy attenuation coefficients among different tissues. Photon-counting spectral CT, with its superior spatial resolution, higher image contrast, and dose efficiency, represents the latest technological advancement in spectral CT. However, sparse angle reconstruction developed to reduce radiation dose leads to stripe artifacts in the images, and photon starvation in different channels of photon-counting spectral CT increases noise and reduces the signal-to-noise ratio. Therefore, designing efficient reconstruction algorithms that combine the characteristics of spectral CT images with depth generation models is crucial to address the problems of insufficient photon count, severe artifacts, and low accuracy at low photon count rates in photon-counting spectral CT imaging.
[0003] Image reconstruction in different energy channels of photon-counting spectral CT can be viewed as a single-energy CT image reconstruction problem. Model-driven sparse optimization algorithms, such as iterative algorithms, TV regularization, dictionary learning, and full-spectrum image prior guidance used in traditional CT, have achieved better results than the FBP analytical reconstruction algorithm. However, these algorithms do not fully consider the non-local similarity and global correlation of images between channels. To characterize the features of spectral CT images and the high-dimensionality of spectral data, more algorithms construct spectral CT images as tensor models, building reconstruction models based on low-rank prior regularization. In general, model-driven reconstruction algorithms have strong interpretability; however, manually designed priors often rely on "subjective assumptions" about the image. These assumptions are difficult to accurately and comprehensively characterize the intrinsic distribution characteristics of the data and are difficult to describe precisely with mathematical formulas, often requiring numerous iterations and hindering efficient numerical computation.
[0004] Given the powerful representation capabilities of neural networks for deep image features, many researchers have begun to utilize deep learning methods for energy spectrum CT image reconstruction. Zhang et al. designed a multi-channel energy spectrum CT image reconstruction framework based on self-supervised learning, achieving good results. Wu et al. explored the organic combination of deep learning and iterative frameworks, as well as the Learning Expert Evaluation-based Reconstruction Network (LEARN) and Plug and Play (PnP) algorithm. However, end-to-end supervised learning image reconstruction requires a large amount of clean datasets as labels, which is difficult to obtain in the medical field due to the difficulty in obtaining high signal-to-noise ratio labeled data. In addition, the interpretability of the neural network structure used is insufficient, and the generalization ability is significantly limited. These unfavorable factors restrict the image reconstruction effect based on deep learning frameworks. Summary of the Invention
[0005] In order to improve the reconstruction effect of spectral CT images while alleviating the dependence on high signal-to-noise ratio labeled data, this invention provides a highly efficient spectral CT sparse reconstruction method and related equipment that integrates subspace representation and fractional generation model to achieve high-quality reconstructed images.
[0006] In a first aspect, the present invention provides a spectral CT sparse reconstruction method that integrates subspace representation and fractional generation model, comprising:
[0007] Step 1: Use a subspace recognition method to obtain the feature images of the spectral CT image and a set of orthogonal bases corresponding to the feature images; the spectral CT image includes images of S channels, where S is an integer greater than 1;
[0008] Step 2: The feature image is denoised using an image denoising method, and the denoised feature image is reconstructed based on the orthogonal basis to generate a first reconstructed energy spectrum CT image;
[0009] Step 3: Input the first reconstructed spectral CT image into the trained score generation model to generate the second reconstructed spectral CT image;
[0010] Step 4: Determine whether the quality of the second reconstructed spectral CT image meets the preset requirements. If not, return to step 2; otherwise, output the second reconstructed spectral CT image at this time.
[0011] Furthermore, the subspace identification method employs a hyperspectral signal identification method based on minimum error.
[0012] Furthermore, the image denoising method employs the block matching and 3D filtering BM3D algorithm.
[0013] Furthermore, during the training of the score generation model, the score generation model is updated by optimizing a preset objective function; wherein the objective function is:
[0014]
[0015] Where A represents the system matrix, x s Let y represent the s-th channel of the spectral CT image χ. s This represents the projection data corresponding to the s-th channel, ||·|| F Let Frobenius norm be denoted, Φ(·) represent the image reconstruction process of the fractional generation model, X is the representation of the χ projection of the energy spectrum CT image in the subspace, λ and β represent the non-negative regularization parameters, Z represents the feature image, and E represents a set of regularized bases corresponding to the feature image.
[0016] Furthermore, the objective function is optimized using the augmented Lagrange multiplier method, specifically including:
[0017] First, rewrite the objective function as the following first intermediate function:
[0018]
[0019] in, This indicates that it is an introduced auxiliary variable;
[0020] The first intermediate function is then rewritten as the second intermediate function as follows:
[0021]
[0022] Where Λ represents the Lagrange multiplier and ρ represents the non-negative penalty parameter;
[0023] The second intermediate function is solved using the alternating direction method; the iterative formula is as follows:
[0024]
[0025] Where, χ k+1 This represents the reconstructed spectral CT image from this round.
[0026] In a second aspect, the present invention provides a spectral CT sparse reconstruction device that integrates subspace representation and fractional generation model, comprising:
[0027] The subspace recognition module is used to obtain the feature image of the energy spectrum CT image and a set of orthogonal bases corresponding to the feature image using the subspace recognition method; the energy spectrum CT image includes an image with S channels, where S is an integer greater than 1;
[0028] The first reconstruction module is used to denoise the feature image using an image denoising method, and to reconstruct the denoised feature image based on the orthogonal basis to generate a first reconstructed energy spectrum CT image.
[0029] The second reconstruction module is used to input the first reconstructed spectral CT image into the trained score generation model to generate the second reconstructed spectral CT image.
[0030] The judgment module is used to determine whether the quality of the second reconstructed energy spectrum CT image meets the preset requirements.
[0031] Thirdly, the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method as described in the first aspect.
[0032] Fourthly, the present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method described in the first aspect.
[0033] The beneficial effects of this invention are as follows:
[0034] To address the issues of severe artifacts and image quality degradation in sparse image reconstruction of photon-counting spectral CT images, this invention provides a sparse reconstruction method for spectral CT that integrates subspace representation and fractional generation models. Subspace representation explores the characterization of global correlation in spectral CT images, decomposing low-rank spectral CT images into the product of feature images and orthogonal bases of subspaces. This representation effectively extracts the main features and global contour structure of the image, providing a more comprehensive characterization of global correlation. The fractional generation model encodes the data distribution structure of the spectral CT image, effectively extracting complex details and textures while preserving edge information, thus highly characterizing the spatial sparse features within the spectral CT image channels. Furthermore, this invention employs a sequential combination of subspace representation and fractional generation models, retaining their respective advantages and mutually promoting each other to improve image reconstruction quality. From the perspective of image reconstruction visualization and evaluation metrics, this fusion approach outperforms the reconstruction results achieved by using fractional generation models alone in comparative algorithms. Attached Figure Description
[0035] Figure 1 One of the flowcharts for the spectral CT sparse reconstruction method that integrates subspace representation and fraction generation model provided in the embodiments of the present invention;
[0036] Figure 2 The second schematic diagram of the spectral CT sparse reconstruction method that integrates subspace representation and fraction generation model provided in this embodiment of the invention;
[0037] Figure 3 A comparison of the reconstruction results of preclinical data using the present invention and the comparative method is provided for embodiments of the present invention.
[0038] Figure 4 This invention provides a comparison of reconstruction results of actual data using the present invention and a comparative method, respectively, for embodiments of the invention.
[0039] Figure 5 A comparison of the reconstruction results of preclinical data material images using the present invention and a comparative method, respectively, provided for embodiments of the present invention;
[0040] Figure 6 A schematic diagram of the structure of the spectral CT sparse reconstruction device that integrates subspace representation and fraction generation model provided in an embodiment of the present invention;
[0041] Figure 7A structural block diagram of an electronic device provided in an embodiment of the present invention;
[0042] Among them, Figure 3 , Figure 4 and Figure 5 In the diagram: the first column is the reference image, the last column is the reconstruction result image of the method of the present invention, and the other columns are the reconstruction result images of the comparison method. Detailed Implementation
[0043] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.
[0044] Fraction generation models have attracted much attention due to their powerful ability to represent image data distributions, pattern coverage, and stable training processes, and are applied to various aspects of image processing. Fraction generation models involve diffusion and sampling processes. Diffusion is the process of adding noise to a clean image to disrupt its data distribution structure; while sampling can be seen as an image reconstruction process, gradually reducing noise in the noisy image until the original image distribution structure is restored. Compared with prior regularization models and end-to-end supervised learning, fraction generation models combine the advantages of both model-driven and data-driven approaches, thus possessing great application potential. However, fitting the fraction function, i.e., the gradient of the probability distribution of image data, to a parameterized neural network requires thousands of training epochs and diverse training samples, resulting in significant computational overhead. To alleviate the pressure of constructing datasets, and inspired by the characteristics of multi-energy spectral CT image data, some researchers have introduced deep learning optimization methods based on model priors. These methods incorporate trained deep networks into the model optimization framework for multi-energy spectral CT image reconstruction. Compared with model-based or supervised learning-based reconstruction algorithms, this method enhances the interpretability and generalization ability of the neural network; however, this method largely depends on the design of the denoising deep network. In this invention, by combining the advantages of both model-driven and data-driven methods, a highly efficient photon-counting spectral CT image reconstruction method is provided, effectively solving the aforementioned problems.
[0045] Combination Figure 1 and Figure 2 As shown, this invention provides a spectral CT sparse reconstruction method that integrates subspace representation and fractional generation model, comprising the following steps:
[0046] S101: The feature image of the energy spectrum CT image and a set of orthogonal bases corresponding to the feature image are obtained by using the subspace recognition method; the energy spectrum CT image includes an image with S channels, where S is an integer greater than 1;
[0047] Specifically, in this embodiment, the subspace identification method adopts the Hyperspectral Signal Identification by Minimum Error (HySime) method. This method first estimates the correlation matrix between the signal and noise, and then selects the subset of eigenvalues that best represent the signal subspace in the sense of least squares error as the feature image.
[0048] S102: The feature image is denoised using an image denoising method, and the denoised feature image is reconstructed based on the orthogonal basis to generate a first reconstructed energy spectrum CT image;
[0049] Specifically, in this embodiment, the image denoising method employs the block matching and 3D filtering BM3D algorithm. The algorithm process includes: first, given a reference image block p in the feature image... i,j Block matching technology is used to extract the p-value within the first channel of the input energy spectrum CT image. i,j Similar image patches are grouped into a set for filtering and noise reduction. Then, the position of the reference image patch is changed, and the above process is repeated to obtain different sets of image patches. This step is repeated on different feature images, and the denoised feature images are reconstructed into a spectral CT image, which is the first reconstructed spectral CT image. This step utilizes the low-rank property of spectral CT images.
[0050] S103: Input the first reconstructed spectral CT image into the trained score generation model to generate the second reconstructed spectral CT image;
[0051] S104: Determine whether the quality of the second reconstructed energy spectrum CT image meets the preset requirements. If not, return to step 2; otherwise, output the second reconstructed energy spectrum CT image at this time.
[0052] Specifically, in this embodiment, it is set that if the reconstructed image in this round has no significant change compared with the previous reconstructed image, then the reconstructed image in this round is considered to meet the quality requirements. It can be understood that when performing the reconstruction in step 103 for the first time, the previous reconstructed image refers to the first reconstructed energy spectrum CT image generated in step S102.
[0053] To address the issues of severe artifacts and image quality degradation in sparse image reconstruction of photon-counting spectral CT, this invention provides a sparse reconstruction method for spectral CT that integrates subspace representation and a fractional generation model. Subspace representation explores the characterization of global correlation in spectral CT images, decomposing low-rank spectral CT images into the product of feature images and orthogonal bases of subspaces. This representation effectively extracts the main features and global contour structure of the image, providing a more comprehensive characterization of global correlation. The fractional generation model encodes the data distribution structure of the spectral CT image, effectively extracting complex details and textures while preserving edge information, thus highly characterizing the spatial sparse features within the spectral CT image channels. Furthermore, this invention employs a sequential combination of subspace representation and the fractional generation model, retaining their respective advantages and mutually promoting each other to improve image reconstruction quality. From the perspective of image reconstruction visualization and evaluation metrics, this fusion approach outperforms the reconstruction results achieved by using the fractional generation model alone in comparative algorithms.
[0054] In one embodiment, when training the score generation model, the score generation model is updated by optimizing a preset objective function; wherein the objective function is:
[0055]
[0056] Where A represents the system matrix, used to convert CT images into projection data; x s y represents the s-th channel of the spectral CT image χ, i.e., the CT image at the s-th energy; s This represents the projection data corresponding to the s-th channel, ||·|| F Let Frobenius norm be denoted, Φ(·) represent the image reconstruction process of the fractional generation model, X is the representation of the χ projection of the energy spectrum CT image in the subspace, λ and β represent the non-negative regularization parameters, Z represents the feature image, and E represents a set of regularized bases corresponding to the feature image.
[0057] In one embodiment, the objective function is optimized using the augmented Lagrange multiplier method, specifically including:
[0058] First, rewrite the objective function as the following first intermediate function:
[0059]
[0060] in, This indicates that it is an introduced auxiliary variable;
[0061] The first intermediate function is then rewritten as the second intermediate function as follows:
[0062]
[0063] Where Λ represents the Lagrange multiplier and ρ represents the non-negative penalty parameter;
[0064] The second intermediate function is solved using the alternating direction method; the iterative formula is as follows:
[0065]
[0066] Where, χ k+1 This represents the reconstructed spectral CT image from this round.
[0067] Specifically, in this embodiment, the learning rate used for training the score generation model is 1×10⁻⁶. -3 The training epochs are 100, the batch size is 1, and the training time is approximately 300 hours.
[0068] To verify the effectiveness of the method of the present invention, a comparative experiment is also provided, and the experimental results are as follows: Figure 3 , Figure 4 and Figure 5 As shown.
[0069] Based on the same inventive concept, such as Figure 6 As shown, this embodiment of the invention provides a spectral CT sparse reconstruction device that integrates subspace representation and fraction generation model, including: a subspace identification module, a first reconstruction module, a second reconstruction module, and a judgment module.
[0070] Specifically, the subspace recognition module is used to obtain feature images of the energy spectrum CT image and a set of orthogonal bases corresponding to the feature images using a subspace recognition method; the energy spectrum CT image includes images with S channels, where S is an integer greater than 1. The first reconstruction module is used to denoise the feature images using an image denoising method, and reconstruct the denoised feature images based on the orthogonal bases to generate a first reconstructed energy spectrum CT image. The second reconstruction module is used to input the first reconstructed energy spectrum CT image into a trained score generation model to generate a second reconstructed energy spectrum CT image. The judgment module is used to determine whether the quality of the second reconstructed energy spectrum CT image meets preset requirements.
[0071] The energy spectrum CT sparse reconstruction device that integrates subspace representation and fractional generation model provided in this embodiment of the invention is for implementing the above method. Its specific functions can be referred to in the above method embodiments, and will not be repeated here.
[0072] Figure 7 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 7As shown, the electronic device may include: a processor 701, a communication interface 702, a memory 703, and a communication bus 704. The processor 701, communication interface 702, and memory 703 communicate with each other via the communication bus 704. The processor 701 can call logical instructions in the memory 703 to execute a sparse reconstruction method for spectral CT. This method includes: obtaining feature images of the spectral CT image and a set of orthogonal bases corresponding to the feature images using a subspace recognition method; the spectral CT image includes images with S channels, where S is an integer greater than 1; denoising the feature images using an image denoising method, and recombining the denoised feature images based on the orthogonal bases to generate a first reconstructed spectral CT image; inputting the first reconstructed spectral CT image into a trained score generation model to generate a second reconstructed spectral CT image; determining whether the quality of the second reconstructed spectral CT image meets preset requirements; if not, returning to step 2; otherwise, outputting the second reconstructed spectral CT image at this time.
[0073] Furthermore, when the logical instructions in the aforementioned memory 703 are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.
[0074] This invention also provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions, and when the program instructions are executed by a computer, the computer can execute the spectral CT sparse reconstruction method provided in the above-described method embodiments.
[0075] This invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the spectral CT sparse reconstruction method provided in the above-described method embodiments.
[0076] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.
[0077] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for sparse reconstruction of spectral CT by fusing subspace representation and fractional generation model, characterized in that, include: Step 1: Use a subspace recognition method to obtain the feature images of the spectral CT image and a set of orthogonal bases corresponding to the feature images; the spectral CT image includes images of S channels, where S is an integer greater than 1; Step 2: The feature image is denoised using an image denoising method, and the denoised feature image is reconstructed based on the orthogonal basis to generate a first reconstructed energy spectrum CT image; Step 3: Input the first reconstructed spectral CT image into the trained score generation model to generate the second reconstructed spectral CT image; Step 4: Determine whether the quality of the second reconstructed spectral CT image meets the preset requirements. If not, return to step 2; otherwise, output the second reconstructed spectral CT image at this time.
2. The spectral CT sparse reconstruction method according to claim 1, characterized in that, The subspace identification method adopts a hyperspectral signal identification method based on minimum error.
3. The spectral CT sparse reconstruction method according to claim 1, characterized in that, The image denoising method described employs the block matching and 3D filtering BM3D algorithm.
4. The spectral CT sparse reconstruction method according to claim 1, characterized in that, When training the score generation model, the score generation model is updated by optimizing a preset objective function; wherein the objective function is: Where A represents the system matrix, x s Representing spectral CT images The s-th channel, y s This represents the projection data corresponding to the s-th channel, ||·|| F Let Frobenius norm be denoted, Φ(·) represent the image reconstruction process of the fractional generation model, and X be the energy spectrum CT image. The projection is represented in the subspace, where λ and β represent nonnegative regularization parameters, Z represents the feature image, and E represents a set of regularized bases corresponding to the feature image.
5. The spectral CT sparse reconstruction method according to claim 4, characterized in that, The objective function is optimized using the augmented Lagrange multiplier method, specifically including: First, rewrite the objective function as the following first intermediate function: in, This indicates that it is an introduced auxiliary variable; The first intermediate function is then rewritten as the second intermediate function as follows: Where Λ represents the Lagrange multiplier and ρ represents the non-negative penalty parameter; The second intermediate function is solved using the alternating direction method; the iterative formula is as follows: in, This represents the reconstructed spectral CT image from this round.
6. A spectral CT sparse reconstruction device that integrates subspace representation and fractional generation model, characterized in that, include: The subspace recognition module is used to obtain the feature image of the energy spectrum CT image and a set of orthogonal bases corresponding to the feature image using the subspace recognition method; the energy spectrum CT image includes an image with S channels, where S is an integer greater than 1; The first reconstruction module is used to denoise the feature image using an image denoising method, and to reconstruct the denoised feature image based on the orthogonal basis to generate a first reconstructed energy spectrum CT image. The second reconstruction module is used to input the first reconstructed spectral CT image into the trained score generation model to generate the second reconstructed spectral CT image. The judgment module is used to determine whether the quality of the second reconstructed energy spectrum CT image meets the preset requirements.
7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 5.
8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 5.