Sparse bimodal kernel method for low dose high quality pet image reconstruction

Abstract

The application relates to the technical field of medical imaging, and discloses a sparse bimodal kernel method for low-dose high-quality PET image reconstruction, which comprises the following steps: defining input parameters such as a PET system matrix and projection data; reconstructing a PET preliminary image based on a kernel-free high-order total variation regularization method, and constructing a PET channel kernel matrix based on a traditional Gaussian kernel and an MRI original image and a modified Gaussian kernel with a gray difference term; generating a weighted matrix through a binary image, fusing two channel kernel matrices to obtain a bimodal kernel matrix; constructing an optimization model containing sparse constraints and non-negative constraints, and iteratively solving the optimization model by using a PKMA algorithm combined with preconditioning technology and KM momentum acceleration; and finally outputting a high-quality reconstructed image. The application can inhibit noise, retain lesion details, balance image quality and calculation efficiency, and meet the high requirements of clinical diagnosis on PET images under a low-dose condition.

Description

Technical Field

[0001] This invention belongs to the field of medical imaging technology, specifically relating to a sparse dual-modal kernel method for low-dose, high-quality PET image reconstruction. Background Technology

[0002] Positron emission tomography (PET) is a key imaging technique in the medical field used to estimate the distribution of specific tracers in the human body. With its ability to capture functional information, it has become an important tool for early disease prevention and diagnosis in clinical practice, and its applications are gradually expanding to the development of treatment plans and the evaluation of treatment efficacy. Through PET imaging, doctors can accurately locate potential lesions in the early stages of disease, providing strong support for the subsequent development of personalized treatment plans and the control of disease progression, which is of great significance for improving patient treatment outcomes.

[0003] In clinical practice, to protect patient health and avoid adverse effects from excessive radionuclide doses, the amount of tracer used in PET imaging is usually controlled. However, this necessary limitation also brings data quality issues: after the tracer enters the body, it undergoes metabolism and physical attenuation, significantly weakening the radionuclide signal it carries. Simultaneously, limited by the hardware performance and imaging principles of PET equipment, a large amount of noise is inevitably introduced during the scanning process, ultimately resulting in high-noise, low-resolution data. This poses a significant challenge to the accuracy and clarity of subsequent image reconstruction and also affects the accuracy of clinical diagnosis, becoming a major bottleneck restricting the clinical application of PET technology. To overcome the quality limitations of low-dose PET imaging, the integration of multimodal information (such as combining high-resolution structural information from MRI images) has become a research hotspot. However, current multimodal fusion technology faces a core contradiction in PET image reconstruction—it is difficult to simultaneously balance image quality and computational efficiency: if higher image detail fidelity is pursued, complex computational models are often required, leading to a significant increase in computation time; if the focus is on improving computational speed, problems such as incomplete image noise suppression and loss of structural information may occur, failing to meet the stringent image quality requirements of clinical diagnosis.

[0004] Existing kernel methods for PET image reconstruction also have significant drawbacks. While traditional Gaussian kernel methods possess good smoothing properties and numerical stability, their fixed kernel structures lack adaptability to different anatomical regions of the human body. For example, when dealing with complex structures such as brain tissue and organ margins, they cannot dynamically adjust kernel parameters based on regional characteristics, resulting in reconstructed images that fail to accurately match the actual anatomical structures. Furthermore, these methods generally ignore the sparsity characteristics and physical constraints of images, further exacerbating the loss of detail, noise residue, and even the appearance of non-physical pixel values ​​(such as negative pixel values) in the reconstruction results, severely violating the physical laws of PET imaging.

[0005] When solving high-dimensional constrained optimization problems related to PET image reconstruction, the limitations of traditional iterative algorithms become even more apparent. These algorithms converge slowly when processing large-scale imaging data, often requiring numerous iterations to approach the optimal solution. This not only consumes excessive computational resources but also significantly prolongs the waiting time for clinical imaging. Furthermore, the algorithms are prone to oscillations during iteration, leading to insufficient reconstruction stability and making it difficult to consistently output high-quality, highly consistent image results under low-dose data conditions.

[0006] In summary, current PET image reconstruction technology faces three core challenges under low-dose conditions: image quality (detail fidelity, noise suppression), computational efficiency (convergence speed, resource consumption), and physical consistency (no abnormal pixel values). Developing a PET image reconstruction method that can effectively integrate multimodal information, possess adaptive adjustment capabilities, and balance quality and efficiency is a key direction for addressing the pain points of clinical low-dose PET imaging and promoting the further widespread application of PET technology. Summary of the Invention

[0007] The present invention aims to address the technical problems of existing low-dose PET imaging, including data quality defects, quality and efficiency imbalance in multimodal fusion, poor adaptability and lack of constraints in traditional kernel methods, low efficiency and insufficient stability of iterative algorithms, defects in kernel matrix reference image quality, and limitations in image reconstruction accuracy, detail fidelity and clinical applicability caused by unreasonable reconstruction initialization and constraint fusion.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A sparse bimodal kernel method for low-dose, high-quality PET image reconstruction includes the following steps:

[0010] S1, Input Data Definition

[0011] Input PET system matrix Projection data Background noise term Preliminary PET images reconstructed using the nucleus-free HOTV method ; MRI raw images ; kernel width parameter The number of neighborhood similar voxels used for kernel matrix sparsification Used to construct weighted matrices threshold Weighting coefficients Step size parameter KM iteration parameters ; Number of non-zero sparse constraints Maximum number of iterations ;in, For the dimensions of the projected data, To reconstruct the total number of voxels in the image;

[0012] S2, PET channel kernel matrix MRI channel kernel matrix Build

[0013] based on Compared to the traditional Gaussian kernel function, it preserves the neighborhood of each voxel. Construct the PET channel kernel matrix using the most similar voxels. ;based on And a modified Gaussian kernel function that introduces a gray-level difference term preserves the value within the neighborhood of each voxel. Construct the MRI channel kernel matrix using the most similar voxels. ;

[0014] S3, dual-modal kernel matrix Fusion

[0015] Using threshold right Generate a binary image B, setting the voxel value of the lesion region to 1 and the background region to 0; construct weighted matrices based on B. and ;in Zhongruo , Otherwise ; Zhongruo , Otherwise ;

[0016] Will and , and After multiplying them separately, they are concatenated column by column to form a bimodal kernel matrix. ;

[0017] S4. Construction of Sparse Optimization Model

[0018] A PET image reconstruction optimization model is constructed, incorporating prior information from PET and MRI, sparse constraints, and non-negativity constraints. The non-negativity constraints are used to ensure the physical plausibility of the reconstruction results. Kernel sparse vectors are initialized. Auxiliary variables and reconstructed images in Based on the circular field of view (FOV) constraint setting of the PET system, the voxel value inside the FOV is the true average photon pair count (TMC), and the value outside the FOV is 0.

[0019] S5. Solving using the preconditional KM iterative algorithm (PKMA)

[0020] During the iteration process, the precondition matrix is ​​calculated first. Then solve for the gradient of the fidelity term. Through hard threshold operation Obtain the intermediate kernel sparse vector The intermediate auxiliary variable is obtained by combining the auxiliary variable update formula. Introducing KM momentum to accelerate updates and Finally, the reconstructed image is calculated. The preconditioned KM iterative algorithm PKMA is an algorithm that combines the fixed-point algorithm, KM momentum acceleration and preconditioning techniques.

[0021] S6, Output reconstructed image

[0022] Iterate to the maximum number of times Output reconstructed image .

[0023] Preferably, in step S2, the traditional Gaussian kernel function expression is: ;in, For kernel width parameter, Voxel representation and The Euclidean distance between the neighborhood feature vectors;

[0024] The modified Gaussian kernel function expression is: ;in, and These represent the MRI images, respectively. and the Gray value of an individual element.

[0025] Preferably, in step S3, the dual-modal kernel matrix During the construction process, the PET channel kernel matrix For the initial image construction of PET without kernel HOTV regularization, the kernel matrix elements satisfy:

[0026]

[0027] voxels of Similar voxel index set, A traditional Gaussian kernel is used to preserve lesion-specific structural information;

[0028] MRI channel kernel matrix Based on the modified Gaussian kernel construction, the kernel matrix elements satisfy:

[0029]

[0030] A modified Gaussian kernel is used to preserve high-resolution local texture and edge information; the two are then weighted and concatenated to form... This achieves the complementary integration of structural and detailed information.

[0031] Preferably, in step S5, the precondition matrix The calculation process is as follows:

[0032] First calculate the vector , Dual-mode kernel matrix The number of columns; satisfy:

[0033]

[0034] Let p be a p-dimensional vector with all elements equal to 1, where p is the dimension of the projected data.

[0035] Calculate the true average photon pair count Where ACTc is the total attenuation correction true count, NPFOV is the number of pixels within the circular field of view (FOV) of the PET system, and NPA is the number of projection angles of the PET scan.

[0036] set up ,final

[0037]

[0038] in For elements all equal to 1 dimensional vector, This indicates that the input vector is converted into a diagonal matrix.

[0039] Preferably, in step S5, the gradient of the fidelity term The expression is:

[0040]

[0041] in, It is a dual-modal kernel matrix. The PET system matrix (describing the physical relationship between tracer distribution and detector signal, the first...) ,j represents the j-th voxel emitting a photon pair with the j-th voxel. (Probability of capture by each detector) Let p be a p-dimensional vector whose elements are all 1. Collected PET projection data, For background noise, This is the estimated value of the PET projection in the kernel representation under the current iteration.

[0042] Preferably, in step S5, a hard threshold operation is performed. The implementation method is as follows:

[0043] Calculate vectors ,in , Preset condition matrix The diagonal elements;

[0044] right Sort by absolute value in descending order and select the top... The index set corresponding to each element ;

[0045] for China belongs to Elements retain their original values ​​and do not belong to Set the element to 0 to get ;

[0046]

[0047] Preferably, in step S5, the auxiliary variable update formula first calculates... ;in , diagonal matrix The largest diagonal element, Let K be the 2-norm of the kernel moment K, and then through Update auxiliary variables. This indicates that the minimum value of each element is taken as the smaller value than 0.

[0048] Preferably, in step S5, the parameters of KM momentum acceleration are... The calculation formula is ,in , To preset the KM iteration parameters, This represents the current iteration number; the update formula is: ; By introducing historical iteration information, iterative oscillations are reduced and the convergence speed is accelerated.

[0049] Preferably, in step S5, during the image reconstruction initialization process, TMC calculates the initial image using PET system projection data and imaging parameters. The voxel values ​​inside the FOV are set to TMC and outside the FOV to 0, ensuring that the initial values ​​meet the physical constraint of PET imaging that "the detector can only cover and reconstruct the target area inside the FOV, and there is no effective projection data outside the FOV", thereby improving the iterative convergence efficiency.

[0050] Preferably, the imaging parameters include the number of projection angles, photon attenuation correction factor, system response function, and background noise model, wherein the system response function is used to construct the PET system matrix and describe the physical relationship between tracer distribution and detector signal.

[0051] Compared with the prior art, the technical effects and advantages of the present invention are:

[0052] This invention effectively addresses the core pain point of data quality defects in low-dose PET imaging, overcoming the bottleneck of traditional low-dose imaging where "noise suppression and detail preservation are difficult to achieve simultaneously." Traditional low-dose PET imaging, due to tracer dosage control, easily leads to high noise and low resolution in the acquired data. This invention, however, fuses complementary information from PET and MRI using a dual-modal kernel matrix—the PET channel kernel matrix preserves lesion-specific structures, while the MRI channel kernel matrix introduces high-resolution textures and edge features. Simultaneously, non-negative constraints avoid non-physical pixel values, and sparse constraints control model complexity. Ultimately, while suppressing noise, it accurately restores lesion details and tissue boundaries, significantly improving the clinical diagnostic usability of the reconstructed images.

[0053] This invention achieves a key breakthrough in balancing efficiency and quality in multimodal information fusion. Existing multimodal fusion technologies often fall into the dilemma of "pursuing quality at the expense of computational complexity, and prioritizing efficiency at the expense of quality degradation." This invention, however, significantly reduces the storage and computational complexity of the kernel matrix by using kernel matrix sparsification (retaining only the most similar voxels in the neighborhood) and dynamic adaptation of the weighted matrix (distinguishing between lesions and background regions). Simultaneously, the preconditioned KM iterative algorithm (PKMA) combines preconditioning techniques with KM momentum acceleration to effectively improve the ill-conditioned nature of high-dimensional optimization problems, reduce iterative oscillations, and accelerate convergence. While ensuring high image quality, it significantly improves computational efficiency, meeting the clinical demand for imaging speed.

[0054] This invention represents an innovative upgrade in the adaptability and constraint integrity of kernel methods. Traditional kernel methods often employ fixed kernel structures, which cannot adapt to the complex differences in human anatomical regions and frequently ignore image sparsity and physical constraints, leading to loss of detail or the appearance of non-physical values ​​in the reconstruction results. This invention designs differentiated kernel functions for the image characteristics of PET and MRI. A traditional Gaussian kernel is customized for preliminary PET images to highlight lesions, while a modified Gaussian kernel with grayscale difference terms is designed for MRI images to protect fine structures. Simultaneously, sparsity constraints and non-negativity constraints are integrated into the optimization model. The sparsity constraints suppress irrelevant noise and preserve key features, while the non-negativity constraints ensure that the results conform to the physical laws of PET imaging, making the reconstructed images closer to the real anatomical structures.

[0055] From a clinical application perspective, this invention demonstrates greater practicality and stability. Traditional iterative algorithms are prone to slow convergence and oscillating results with low-dose data. This invention, through the synergy of physical constraint initialization (setting initial values ​​based on FOV and the true average photon pair count) and the PKMA algorithm, not only improves the stability of iterative convergence but also ensures that the initial estimate closely approximates the true tracer distribution, reducing the accumulation of iterative errors. Furthermore, the weighted fusion strategy of the dual-modal kernel can dynamically adjust weights according to the characteristics of the lesion and background regions, achieving high-quality reconstruction for lesions of different anatomical locations and sizes, thus broadening its applicability and providing more reliable imaging support for early clinical disease diagnosis and treatment planning. Attached Figure Description

[0056] Figure 1 This invention provides high-quality clinical PET brain images.

[0057] Figure 2 This invention provides high-quality clinical MRI brain images;

[0058] Figure 3 This is a graph showing the pixel grayscale distribution of grayscale profiles of the nucleus-free HOTV method, PET single-core method, MRI single-core method, and sparse dual-core method under high-dose conditions according to the present invention.

[0059] Figure 4 This is a graph showing the pixel grayscale distribution of grayscale profiles of the nucleus-free HOTV method, PET single-core method, MRI single-core method, and sparse dual-core method under low-dose conditions according to the present invention.

[0060] Figure 5 This is a graph showing the PSNR values ​​of the nucleus-free HOTV method, PET single-nucleus method, MRI single-nucleus method, and sparse dual-nucleus method under high-dose conditions of the present invention as a function of the number of iterations.

[0061] Figure 6 This is a graph showing the PSNR values ​​of the nucleus-free HOTV method, PET single-nucleus method, MRI single-nucleus method, and sparse dual-nucleus method under low-dose conditions of the present invention as a function of the number of iterations.

[0062] Figure 7 This is a reconstructed image of the nucleus-free HOTV method under high-dose conditions according to the present invention;

[0063] Figure 8 This is a reconstructed image of the PET single-core method under high-dose conditions according to the present invention;

[0064] Figure 9 These are reconstructed images from the high-dose MRI single-nucleus method of this invention;

[0065] Figure 10 This is a reconstructed image of the sparse dual-core method under high-dose conditions according to the present invention;

[0066] Figure 11 This is a reconstructed image of the nucleus-free HOTV method under low-dose conditions according to the present invention;

[0067] Figure 12 This is a reconstructed image of the PET single-core method under low-dose conditions according to the present invention;

[0068] Figure 13 These are reconstructed images of the MRI single-nuclear method under low-dose conditions according to the present invention;

[0069] Figure 14 This is a reconstructed image of the sparse dual-core method under low-dose conditions according to the present invention;

[0070] Figure 15 Calculate the region image for SSIM in this invention;

[0071] Figure 16 This is a flowchart of the present invention. Detailed Implementation

[0072] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0073] The following combination Figures 1 to 16 This application will be described in further detail;

[0074] The technical solution proposed in this invention is as follows:

[0075] This method first uses raw PET projection data and corresponding MRI images as input. A modified Gaussian kernel function is constructed by extracting structural prior information from the two images. This kernel function is used to introduce structural constraints and maintain image smoothness during reconstruction. Simultaneously, the number of parameters and computational complexity are reduced by sparsifying the kernel matrix, while enhancing the preservation of important features and suppressing noise interference from irrelevant regions. To further ensure the physical plausibility of the medical imaging results, this invention introduces non-negativity constraints to avoid non-physical pixel values.

[0076] In the solution process, this invention unifies the aforementioned sparse bimodal kernel constraints and nonnegativity constraints into an optimization problem, and employs the Krasnosel'skiĭ–Mann (KM) iterative algorithm based on fixed-point theory for solution. To improve the ill-conditioned nature of large-scale imaging problems and accelerate convergence, this invention introduces a precondition matrix into the iterative framework. This precondition matrix can adaptively adjust the gradient direction and step size according to the problem structure, thereby effectively shortening the computation time and improving reconstruction stability. Furthermore, this invention further combines generalized momentum techniques, introducing historical iteration information to reduce oscillations during the iteration process, enhancing the stability and flexibility of the algorithm, and significantly accelerating the convergence speed.

[0077] The specific details of the corresponding models and algorithms are as follows:

[0078] 1. PET Image Reconstruction Model Based on Sparse Dual-Modal Kernel

[0079] PET imaging, as an important functional medical imaging technique, aims to assist in disease diagnosis and treatment by reconstructing the distribution of tracers in the human body. To fully utilize the functional information of PET images and the high-resolution structural information of MRI images, this invention proposes a PET image reconstruction model based on dual-core sparsity constraints. This model comprehensively considers the fidelity of PET data, MRI-guided structural priors, sparsity constraints, and non-negative constraints related to physical consistency.

[0080] Specifically, in setting up a positron emission tomography (PET) system, the dimension of the projected data is... The total number of voxels in the reconstructed image is PET system matrix Used to describe the physical relationship between tracer distribution and detector signal, where the first... The element represents the number of elements from the first element. The photons emitted by the individual element are paired with the first The probability of each detector pair being captured; the background noise vector is The collected PET projection data is The system satisfies the Poisson statistical model:

[0081]

[0082] in Indicates expectation as A Poisson distributed random vector, This represents the tracer distribution image to be reconstructed. The goal of PET image reconstruction is to reconstruct the image based on projection data. Tracer distribution map at the reconstruction site This is a classic inverse problem. For this model, the traditional solution approach is to transform it into a corresponding Poisson maximum likelihood estimation optimization model, i.e., minimizing the following objective function. :

[0083]

[0084] in, Represents the dot product of vectors. Indicates that all elements are 1 dimensional vector, It is the element-wise natural logarithm.

[0085] In order to effectively utilize the structural information of the reference image, this invention firstly... The radial basis function (RBF) Gaussian kernel is constructed from local neighborhood features to measure the structural similarity of different voxels. The traditional Gaussian kernel is defined as:

[0086] (Equation 1)

[0087] in For kernel width parameter, Voxel representation and The Euclidean distance between the neighborhood feature vectors.

[0088] However, extensive experiments have revealed that for small black regions surrounded by gray areas, relying solely on structural similarity metrics leads to the region being "eroded" by the surrounding gray areas during reconstruction, resulting in overly smoothed distortion. To address this issue, this invention introduces a "pixel intensity difference" term into the traditional Gaussian kernel, allowing the kernel function to consider both structural similarity and grayscale differences, thereby better preserving fine structures and edge information. The modified kernel function is defined as follows:

[0089] (Equation 2)

[0090] in and These represent the first and second reference images, respectively. and the The grayscale value of a voxel. To avoid excessive storage and computational overhead in high-dimensional calculations, this invention constructs a kernel matrix... At that time, only the first one is retained. The set of voxel indices most similar to each voxel Its definition is:

[0091] (Equation 3)

[0092] This sparsification strategy not only preserves the most valuable structural similarity information, but also significantly reduces the storage space and computational complexity of the matrix, thereby improving the scalability of the reconstruction algorithm.

[0093] After kernel representation, the PET image is expressed as Combining PET system data with kernel representation, the data fitting term is defined as:

[0094] (Equation 4)

[0095] To control model complexity and suppress noise, the kernel coefficient vector is limited. The sparsity, i.e., the constraint ,in This indicates the number of non-zero elements in the vector. A preset sparsity threshold is set. In addition, non-negative constraints are applied to the reconstructed image in accordance with physical imaging requirements to ensure the physical rationality of the results.

[0096] In summary, the sparse dual-modal kernel PET image reconstruction model proposed in this invention can be represented as the following optimization problem:

[0097] (Equation 5)

[0098] in, The nonnegativity constraint indicator function for the kernel mapping space is defined as:

[0099] (Equation 6)

[0100] in, The sparse constraint indicator function is defined as:

[0101] (Equation 7)

[0102] This model effectively fuses prior structural information through kernel functions, reduces parameter redundancy by utilizing sparse constraints, and combines nonnegative domain constraints to ensure high quality and physical consistency of PET image reconstruction.

[0103] 2. Algorithm for solving the proposed PET image reconstruction model

[0104] Before developing the preconditional KM iterative algorithm (PKMA), we first present the solution of model (5) based on fixed-point iteration. To this end, we let... Indicates all The set of symmetric positive definite matrices. For , -The weighted inner product is defined as , where, for a convex function , exist Regarding The nearest neighbor operator is defined as:

[0105]

[0106] review conjugate function Defined as:

[0107]

[0108] The following is a description of the fixed points of the solution to model (5):

[0109]

[0110] in and Let be the preconditioning matrix. To improve the stability of the iteration, the algorithm is further improved by utilizing the split matrix and implicit scheme iteration techniques as follows:

[0111]

[0112] To further accelerate convergence, Krasnosel'skiĭ–Mann (KM) momentum acceleration is introduced based on fixed-point iteration:

[0113]

[0114] in The iterations gradually increase. This step is equivalent to transforming fixed-point iteration into momentum iteration, thereby reducing oscillations and increasing the iteration speed.

[0115] Let the precondition matrix ,in and It is a positive number. It is A diagonal matrix whose diagonal elements are all positive. In this case, according to the definition of the proximity operator, for ,

[0116]

[0117] By using the well-known Moreau decomposition:

[0118]

[0119] in It is an identity operator, and for The equation

[0120]

[0121] have:

[0122]

[0123] In summary, the iterative process of the PKMA algorithm of this invention is as follows:

[0124]

[0125] Selection of PKMA parameter preconditioning matrix:

[0126] Here, we take vectors satisfy

[0127]

[0128] The precondition matrix is

[0129]

[0130] where constant Set as ,and

[0131]

[0132] TMC (TrueMeanCount) represents the true average photon pair count of the image, where ACTc, NPFOV, and NPA represent the total attenuation-corrected true count, the number of pixels within the circular field of view, and the number of projection angles, respectively.

[0133]

[0134] in diagonal matrix The largest diagonal element.

[0135] 3. Specific Implementation of the Invention

[0136] (1) Gradient of the fidelity term

[0137] In formula (4) The gradient is:

[0138]

[0139] (2) Solving the proximal operator of the sparse constraint indicator function

[0140] Iteration formula middle, The definition of is:

[0141]

[0142] when hour, ;

[0143] when When, diagonal matrix ,but

[0144]

[0145] When minimizing, an index set needs to be selected. (size is) ),for ,make ,for ,make .at this time,

[0146]

[0147] To minimize the above expression, we should choose... Make The largest index contains In the middle. Let the vector elements in , It makes

[0148]

[0149] of Any permutation of . Then we call . for One - The set of indices with the largest absolute value, because The component values ​​may not be completely different, so of - The set of indices for the largest absolute value may not be unique, we use express One - Maximum absolute value index set.

[0150] Therefore when hour,

[0151]

[0152] (3) Solving the proximal operator of the nonnegativity constraint indicator function

[0153] We will now solve for the auxiliary variable iteration in the iterative formula:

[0154]

[0155] Based on the proximal operator and nonnegativity constraint indicator function The definition, for ,

[0156]

[0157]

[0158] (4) Reconstructing the image Initialization

[0159] During PET imaging, the effective reconstruction range of the system is limited by its circular field of view (FOV). That is, the detector can only cover and reconstruct the target area within the FOV, while the area outside the FOV does not physically have valid projection data. Therefore, in the iterative reconstruction algorithm, to accelerate convergence and improve the physical plausibility of the initial estimate, this invention initializes the reconstructed image under physical constraints before the iterative calculation begins.

[0160] Specifically, this invention first calculates the true average photon pair count (TMC) within the field of view (FOV) based on the projection data output by the detector, combined with the imaging parameters of the PET system (including the number of projection angles, photon attenuation correction factor, system response function, and background noise model, etc.). The TMC reflects the average number of true coincidence events per unit time and can characterize, to some extent, the average activity level of the radioactive tracer in the imaged area. Subsequently, the initial image vector... Set to a uniform disk model consistent with the shape of the FOV: the initial value of all pixel (voxel) positions inside the FOV is uniformly assigned to TMC to ensure that the initial distribution is physically consistent with the average activity measured by the system; the pixel positions outside the FOV are set to 0 because the detector cannot collect effective signals, so as to avoid introducing noise interference from invalid areas during the reconstruction process.

[0161] This initialization strategy not only physically conforms to the detection range constraints of PET imaging, but also provides an initial solution that is close to the true distribution in iterative optimization, thereby reducing the convergence time of the algorithm and reducing the risk of getting trapped in local optima.

[0162] (5) Construction of the kernel matrix

[0163] In the construction of the kernel matrix, the quality of the reference image on which the kernel function depends directly affects the structural information that the kernel matrix can express. If the raw low-dose PET image is used directly to construct the kernel matrix, the structural features are often not clear enough due to the strong noise and blur in the image, resulting in insufficient ability of the kernel matrix to characterize the real tissue boundaries, thus affecting the reconstruction accuracy.

[0164] To address this issue, this invention introduces a kernelless HOTV (Higher-Order Total Variation) regularization reconstruction method in the kernel matrix construction of the PET channel to perform preliminary processing on the low-dose PET raw data. HOTV regularization can not only effectively suppress random noise, but also avoid the "staircase effect" common in traditional TV regularization while preserving edge information, thereby obtaining a preliminary reconstructed image with lower noise and clearer structure. Since the overall contrast of the preliminary reconstructed image is limited and the gray-level differences in small areas are not significant, neighborhood relationships can be effectively established simply by relying on structural similarity. Therefore, in the PET channel, this invention adopts the Gaussian kernel function in formula (1), and combines it with formula (3) which only retains the kernel function related to the first... The set of voxel indices most similar to each voxel The method constructs a kernel matrix for PET images based on the kernel-free HOTV regularization reconstruction method. .

[0165] For MRI channels, due to the high spatial resolution and good contrast of the original MRI image, the gray-level changes in local areas are more obvious at the edges and fine structures. If only structural similarity is relied upon, these gray-level differences are easily ignored, resulting in small areas being "eroded" by surrounding similar structures during reconstruction, producing an overly smooth distortion. To avoid this problem, this invention introduces a gray-level difference term (the modified Gaussian kernel function in formula (2)) in the construction of the MRI kernel matrix, and combines formula (3) to retain only the gray-level difference term with the first gray-level difference term. The set of voxel indices most similar to each voxel Constructing the kernel matrix .

[0166] Regarding the construction of dual cores, although there are many options, extensive experimental verification has shown that the core matrix of the PET channels... Kernel matrix with MRI channels A superior PET reconstruction effect can be achieved by simply stitching the columns together. This construction method effectively combines the advantages of both modalities for mutual complementarity. It provides significant lesion features preserved in images reconstructed by the nucleus-free HOTV method. This preserves clear structural boundary information from the MRI images.

[0167] To further enhance the fusion effect, this invention introduces two coefficient matrices before the dual-core splicing. and The two-channel kernel matrix is ​​weighted. Specifically, a grayscale threshold is set for the kernel-free HOTV reconstructed image. Binarize it, and set regions above the threshold. (Corresponding lesion area), areas below the threshold are set as follows: Subsequently, In the middle, the value will be Regional coefficients The value is Regional coefficients ;exist In the middle, the value will be Regional coefficients The value is Regional coefficients Because the contrast of lesions is obvious in PET images reconstructed by the nucleus-free HOTV method, the threshold... This allows for relatively stable setting, thus achieving accurate regional weighting. The final dual-core matrix is ​​defined as follows:

[0168]

[0169] This dual-core matrix combines lesion-specific information with high-resolution structural information while maintaining a simple structure. After multiple iterations of the kernel method, the reconstructed PET image can simultaneously possess the dual advantages of clear lesions and high spatial resolution.

[0170] (6) Specific process of implementing the sparse bimodal kernel method for PET image reconstruction

[0171] ① Input:

[0172] Input system matrix Projection data Background noise term Preliminary PET images reconstructed using the nucleus-free HOTV method ; MRI raw images ; kernel width parameter The number of neighborhood similar voxels used for kernel matrix sparsification Used to construct weighted matrices threshold Weighting coefficients Step size parameter KM iteration parameters ;Sparse constraint: number of non-zero values Maximum number of iterations .

[0173] ② Initialization:

[0174] a. According to The PET channel kernel matrix is ​​calculated using formulas (1) and (3). Only retain the neighborhood of each voxel The element corresponding to the most similar voxel.

[0175] b. According to The MRI channel kernel matrix is ​​calculated using formulas (2) and (3). Also retain The most similar voxel.

[0176] c. Using thresholds right Generate binary image The voxel value of the lesion area is set to 1, and the background area is set to 0.

[0177] d. Construct the weighted matrix If , Otherwise .

[0178] e. Construct the weighted matrix If , Otherwise .

[0179] f. Forming a dual-modal kernel matrix: ,calculate ,calculate .

[0180] g. Initialize the kernel sparse vector Auxiliary variables Set the iteration counter .

[0181] ③ Iterative loop:

[0182]

[0183]

[0184]

[0185]

[0186] #right Apply a hard threshold retention operation, that is, retain the one with the largest weighted absolute value. Set one element to zero and the rest to zero.

[0187]

[0188]

[0189]

[0190]

[0191]

[0192]

[0193]

[0194]

[0195] ④ Output:

[0196] An example of the sparse bimodal kernel method for low-dose, high-quality PET image reconstruction is as follows:

[0197] This embodiment uses a Matlab environment to build a simulation experimental platform to verify the effectiveness of the "Sparse Bimodal Kernel Method for Low-Dose, High-Quality PET Image Reconstruction". The experimental platform is based on the PET imaging simulation system developed by the inventors during their visit to Sloan Kettering Cancer Center in New York, USA, in 2015-2016 (see reference [Y. Lin, CR Schmidtlein, Q. Li, S. Li and Y. Xu. A_Krasnoselskii-Mann Algorithm with an Improved EMPreconditioner for PET Image Reconstruction. IEEETrans. Med. Imag., 2019, 38(9): 2114-2126.], namely [Y. Lin, CR Schmidtlein, Q. Li, S. Li and Y. Xu. A Krasnoselskii-Mann Algorithm with an Improved EM Preconditioner for PET Image Reconstruction. IEEETrans. Med. Imag., 2019, 38(9): 2114-2126.]). [2114-2126.], using a brain phantom to simulate a clinical PET imaging scenario, the reconstruction effects of different algorithms under low-dose and high-dose conditions were compared. The specific implementation process is as follows:

[0198] The simulation uses a brain phantom as the original image (e.g., Figure 1 , Figure 2 As shown in the figure, reconstruction was performed using a sparse bimodal kernel method under low-dose conditions to verify the effectiveness of the invention. Two white circular regions with different radii were drawn on the same horizontal line of the original image to simulate lesion regions of two different sizes, thereby facilitating a comparison of the performance differences of different algorithms in terms of detail restoration and edge fidelity.

[0199] (2) Figure 3 and Figure 4 The study documented four methods at low doses (1.7 × 10⁻⁶): nucleus-free HOTV method, sparse mononuclear method using PET images, sparse mononuclear method using MRI images, and sparse bimodal nucleus method described in this patent. 6 ) and high dose (6.8×10 6 Under the condition of ), the pixel grayscale distribution along the grayscale profile passing through the two white circles mentioned above (the horizontal axis is the horizontal axis of the image, and the vertical axis is the grayscale value).

[0200] Figure 5 and Figure 6 The curves showing the peak signal-to-noise ratio (PSNR) of four different algorithms as a function of the number of iterations are compared.

[0201] Figures 7 to 14 A comparison of the reconstruction results of four algorithms after 300 iterations is presented. The results show that the sparse bimodal kernel method of this invention outperforms other algorithms in terms of lesion edge and detail rendering, obtaining clearer and more detailed reconstructed images. Tables 1 and 2 record the comparison of the structural similarity index (SSIM) and normalized relative contrast (NRC) at the end of the iteration for the four algorithms under high and low dose conditions, respectively; where the small region selected for calculating SSIM is as follows... Figure 15 As shown, red represents the structural area, and orange represents the background area.

[0202] Table 1. Comparison of NRC and SSIM methods after 300 iterations under high-dose conditions.

[0203] method Nuclear-free HOTV law PET mononuclear method MRI single-core method Sparse dual-core method NRC 0.75 0.79 0.10 0.88 SSIM 0.25 0.27 0.71 0.73

[0204] Table 2 Comparison of NRC and SSIM methods after 300 iterations under low-dose conditions

[0205] method Nuclear-free HOTV law PET mononuclear method MRI single-core method Sparse dual-core method NRC 0.68 0.76 0.14 0.86 SSIM 0.25 0.26 0.67 0.70

[0206] The experimental results show that the sparse dual-kernel method proposed in this invention can maintain high reconstruction quality even under low-dose conditions, with its PSNR, SSIM, and NRC evaluation metrics all outperforming the comparative algorithms. Furthermore, the reconstruction results demonstrate outstanding performance in detail fidelity and edge sharpness, effectively suppressing noise and artifacts. This advantage stems from the ability of sparsity constraints to suppress irrelevant noise and the complementarity of the sparse dual-kernel method in characterizing image structure and texture features, thus achieving a dual improvement in image quality and detail recovery capability.

[0207] This invention effectively solves the core problem of "difficulty in balancing noise suppression and detail preservation" in low-dose PET imaging, significantly improving image quality and clinical diagnostic value. Traditional low-dose PET imaging, due to tracer dosage control, is prone to high noise and low resolution in the acquired data. However, this invention constructs a dual-modal kernel matrix, fusing lesion-specific structural information from the PET channel with high-resolution texture edge features from the MRI channel. Simultaneously, it introduces non-negative constraints to avoid non-physical pixel values ​​and combines sparse constraints to control model complexity. This efficiently suppresses noise while accurately restoring lesion details and tissue boundaries, making the reconstructed images more closely resemble real anatomical structures and meeting the stringent clinical requirements for lesion identification and boundary judgment.

[0208] This invention achieves breakthroughs in computational efficiency and application stability, balancing clinical applicability with technological innovation. Addressing the shortcomings of existing multimodal fusion technologies ("quality and efficiency imbalance") and traditional iterative algorithms ("slow convergence and oscillations"), this invention reduces computational complexity through kernel matrix sparsification (retaining only neighboring similar voxels), dynamic weighted matrix adaptation (distinguishing lesions from background), and sparse constraints. Combined with the preconditioning techniques and momentum acceleration of the preconditioned KM iterative algorithm (PKMA), it significantly accelerates convergence speed and reduces iterative oscillations. Simultaneously, it initializes images based on the physical constraints of the PET system, ensuring result stability and physical rationality. High-quality reconstruction can be achieved for lesions of different anatomical locations and sizes, providing reliable technical support for efficient early disease diagnosis and treatment planning in clinical practice.

[0209] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A sparse bimodal kernel method for low-dose, high-quality PET image reconstruction, comprising the following steps: S1, Input Data Definition Input PET system matrix Projection data Background noise term Preliminary PET images reconstructed using nucleus-free high-order total variational (HOTV) regularization. ; MRI raw images ; kernel width parameter ; Number of neighborhood similar voxels used for kernel matrix sparsification Used to construct weighted matrices threshold Weighting coefficients; Step size parameter KM iteration parameters ; The number of non-zero constraints for sparseness Maximum number of iterations ;in, For the dimensions of the projected data, To reconstruct the total number of voxels in the image; S2, PET channel kernel matrix MRI channel kernel matrix Build based on Compared to the traditional Gaussian kernel function, it preserves the neighborhood of each voxel. Construct the PET channel kernel matrix using the most similar voxels. ;based on And a modified Gaussian kernel function that introduces a gray-level difference term preserves the value within the neighborhood of each voxel. Construct the MRI channel kernel matrix using the most similar voxels. ; S3, dual-modal kernel matrix Fusion Using threshold right Generate binary image The voxel value of the lesion area is set to 1, and the background area is set to 0; according to Construct weighted matrices respectively and ;in Zhongruo , Otherwise ; Zhongruo , Otherwise ; Will and , and After multiplying them separately, they are concatenated column by column to form a bimodal kernel matrix. ; S4. Construction of Sparse Optimization Model A PET image reconstruction optimization model is constructed, incorporating prior information from PET and MRI, sparse constraints, and non-negativity constraints. The non-negativity constraints are used to ensure the physical plausibility of the reconstruction results. Kernel sparse vectors are initialized. Auxiliary variables Auxiliary variables and reconstructed images ,in Based on the circular field of view (FOV) constraint setting of the PET system, the voxel value inside the FOV is the true average photon pair count (TMC), and the value outside the FOV is 0. S5. Solving using the preconditional KM iterative algorithm (PKMA) During the iteration process, the precondition matrix is ​​calculated first. Then solve for the gradient of the fidelity term. Through hard threshold operation Obtain the intermediate kernel sparse vector The intermediate auxiliary variable is obtained by combining the auxiliary variable update formula. Introducing KM momentum to accelerate updates and Finally, the reconstructed image is calculated. The preconditioned KM iterative algorithm PKMA is an algorithm that combines the fixed-point algorithm, KM momentum acceleration and preconditioning techniques. S6, Output reconstructed image Iterate to the maximum number of times Output reconstructed image .

2. The sparse bimodal kernel method for low-dose, high-quality PET image reconstruction according to claim 1, characterized in that: A modified Gaussian kernel function with grayscale difference terms is introduced to construct the kernel matrix; In step S2, the traditional Gaussian kernel function expression is: ;in, For kernel width parameter, Voxel representation and Euclidean distance between neighborhood feature vectors; The modified Gaussian kernel function expression is: ;in, and These represent the MRI images, respectively. and the Gray value of an individual element.

3. The sparse bimodal kernel method for low-dose, high-quality PET image reconstruction according to claim 2, characterized in that: Before the dual-core stitching, a coefficient matrix is ​​introduced to weight the two-channel kernel matrix, ensuring that the dual-core matrix structure is simple while fully combining lesion-specific information and resolution structure information; In step S3, during the construction of the dual-modal kernel matrix, the PET channel kernel matrix is ​​constructed from the kernelless HOTV regularized PET preliminary image, and the kernel matrix elements satisfy: ； voxels of Similar voxel index set, A traditional Gaussian kernel is used to preserve lesion-specific structural information; MRI channel kernel matrix Based on the modified Gaussian kernel construction, the kernel matrix elements satisfy: ； A modified Gaussian kernel is used to preserve high-resolution local texture and edge information; the two are then weighted and concatenated to form... This achieves the complementary integration of structural and detailed information.

4. The sparse bimodal kernel method for low-dose, high-quality PET image reconstruction according to claim 1, characterized in that: An improved precondition matrix was introduced; In step S5, the precondition matrix The calculation process is as follows: First calculate the vector , Dual-mode kernel matrix The number of columns; satisfy: ； For elements all equal to 1 dimensional vector, For the dimensions of the projected data; Calculate the true average photon pair count Where ACTc is the total attenuation correction true count, NPFOV is the number of pixels within the circular field of view (FOV) of the PET system, and NPA is the number of projection angles of the PET scan. set up ,final: ， in For elements all equal to 1 dimensional vector, This indicates that the input vector is converted into a diagonal matrix.

5. The sparse bimodal kernel method for low-dose, high-quality PET image reconstruction according to claim 4, characterized in that: In step S5, the gradient of the fidelity term The expression is: ， in, It is a dual-modal kernel matrix. The PET system matrix (describing the physical relationship between tracer distribution and detector signal, the first...) Element represents the first Individual photons emitted by the first individual photon pair were... (Probability of capture by each detector) For elements all equal to 1 dimensional vector, Collected PET projection data, For background noise, This is the estimated value of the PET projection in the kernel representation under the current iteration.

6. The sparse bimodal kernel method for low-dose, high-quality PET image reconstruction according to claim 5, characterized in that: In step S5, the hard threshold operation is performed. The implementation method is as follows: Calculate vectors ,in , Preset condition matrix The diagonal elements; right Sort by absolute value in descending order and select the top... m The index set corresponding to each element ; for China belongs to Elements retain their original values ​​and do not belong to Set the element to 0 to get ; 。 7. The sparse bimodal kernel method for low-dose, high-quality PET image reconstruction according to claim 6, characterized in that: In step S5, the auxiliary variable update formula first calculates... ;in , diagonal matrix The largest diagonal element, For the kernel matrix The 2-norm, and then through Update auxiliary variables, This indicates that the minimum value of each element is taken as the smaller value than 0.

8. The sparse bimodal kernel method for low-dose, high-quality PET image reconstruction according to claim 7, characterized in that: Utilizing KM momentum acceleration techniques; In step S5, the parameters of KM momentum acceleration The calculation formula is ,in , To preset the KM iteration parameters, This represents the current iteration number; the update formula is: ; By introducing historical iteration information, iterative oscillations are reduced and the convergence speed is accelerated.

9. The sparse bimodal kernel method for low-dose, high-quality PET image reconstruction according to claim 8, characterized in that: The initial image settings are appropriate; In step S5, during the image reconstruction initialization process, TMC calculates the initial image using PET system projection data and imaging parameters. The voxel values ​​inside the FOV are set to TMC and outside the FOV to 0, ensuring that the initial values ​​meet the physical constraint of PET imaging that "the detector can only cover and reconstruct the target area inside the FOV, and there is no effective projection data outside the FOV", thereby improving the iterative convergence efficiency.

10. The sparse bimodal kernel method for low-dose, high-quality PET image reconstruction according to claim 9, characterized in that: Imaging parameters include the number of projection angles, photon attenuation correction factor, system response function, and background noise model. The system response function is used to construct the PET system matrix, which describes the physical relationship between tracer distribution and detector signal.

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