A time-of-flight positron emission tomography reconstruction method and device based on three-dimensional Gaussian representation

Abstract

The application discloses a time-of-flight positron emission tomography reconstruction method and device based on three-dimensional Gaussian representation, which represents the amplitude information of a three-dimensional magnetic resonance image to be reconstructed as an amplitude three-dimensional Gaussian space representation, represents phase information as a combination of a reference phase and a phase residual, models the phase residual by a phase residual three-dimensional Gaussian space representation, and takes a magnetic resonance target slice, a target voxel position or a three-dimensional reconstruction grid as a rendering object. The method combines a predicted complex magnetic resonance image with multi-coil sensitivity map, Fourier encoding, under-sampling mask and k-space data consistency constraints to realize self-supervised reconstruction from multi-coil under-sampling k-space data to a three-dimensional magnetic resonance image. The method can adapt to magnetic resonance layer sampling, three-dimensional body data reconstruction, multi-coil Fourier encoding and complex image reconstruction process, and is suitable for magnetic resonance parallel acceleration imaging under different part and different automatic calibration signal area size conditions of knees, hearts, brains and the like.

Description

Technical Field

[0001] This invention belongs to the field of positron emission tomography and medical image reconstruction, specifically relating to a time-of-flight positron emission tomography reconstruction method based on three-dimensional Gaussian representation, which is particularly suitable for three-dimensional PET image reconstruction under low-dose, low-count, or low signal-to-noise ratio conditions. Background Technology

[0002] Positron emission tomography (PET) can reflect the distribution and metabolic activity of radioactive tracers in human tissues and lesions, and has important applications in tumor staging, treatment evaluation, diagnosis of neurological diseases, and assessment of cardiovascular diseases. PET imaging typically requires the injection of a radioactive tracer into the subject, followed by the acquisition of annihilated photons to form projection data using a detector. Due to limitations such as radiation dose, scan time, detection efficiency, and acquisition count, the actual PET projection data usually contains significant statistical noise. Especially under low-dose or low-count conditions, insufficient photon statistics can lead to increased noise in the reconstructed image, blurred lesion boundaries, loss of fine structures, and decreased quantitative accuracy.

[0003] Existing PET image reconstruction methods mainly include filtered backprojection, maximum likelihood expectation maximization, ordered subset expectation maximization, and maximum a posteriori reconstruction. These methods estimate the three-dimensional radioactivity distribution using PET projection data and the system matrix, but they are susceptible to Poisson noise under low count conditions. With fewer iterations, image detail recovery is insufficient; with more iterations, statistical noise in the projection data may be gradually amplified. Introducing regularization methods such as total variation, spatial smoothing, low-rank sparsity, or kernel constraints can suppress some noise, but excessively strong constraints can lead to overly smoothed local structures, affecting the recovery of small lesions and high-frequency boundaries.

[0004] In recent years, supervised deep learning, deep image priors, and implicit neural representations have been applied to PET image reconstruction. Supervised methods typically require paired low-count PET data and high-quality reference images, and their application is limited by the availability of training data, equipment, scanning protocols, and differences in imaging sites. Unsupervised or self-supervised methods reduce the dependence on paired training data, but convolutional neural network-based methods tend to preferentially fit low-frequency image components. Implicit neural representations based on multilayer perceptrons use global network parameters to describe the three-dimensional activity distribution, which may lead to insufficient local detail recovery, high parameter coupling, and large optimization computations under strong Poisson noise conditions.

[0005] Three-dimensional Gaussian representation describes a continuous three-dimensional space using multiple three-dimensional Gaussian primitives with spatial location, scale, orientation, and intensity parameters, and can control the spatial distribution of different regions using local parameters. Current three-dimensional Gaussian representations are mainly applied to natural scene reconstruction, computed tomography (CT), magnetic resonance imaging (MRI), and dynamic medical image reconstruction. PET imaging differs from the above imaging methods in terms of projection formation process, noise distribution, and data correction methods, requiring the establishment of corresponding forward projection and parameter optimization processes by combining the PET system matrix, time-of-flight response, and correction data for random and scattering events.

[0006] Furthermore, when directly optimizing 3D Gaussian primitives on low-count PET projection data, the 3D Gaussian primitives may fit Poisson noise in the projection data, leading to problems such as local abnormal activity, primitive scale imbalance, or unstable spatial distribution. MRI or CT images can provide high-resolution anatomical information, but structural inconsistencies may exist between different modalities. If anatomical images are directly used to constrain PET reconstruction, non-corresponding structures may be introduced into the PET reconstruction results. Therefore, it is necessary to control the scope and weight of anatomical priors based on the local feature relationships between PET images and anatomical images.

[0007] The existing technology has the following technical problems:

[0008] 1) Existing PET reconstruction methods mainly use fixed voxels or global networks to represent the distribution of radioactivity. It is difficult to independently adjust the local location, scale and orientation according to the spatial morphology of different regions. Therefore, it is difficult to achieve both noise suppression and restoration of small lesions, boundaries and local high-frequency structures under low count conditions.

[0009] 2) Existing three-dimensional Gaussian reconstruction methods lack a data processing chain that matches the physical process of time-of-flight PET imaging, making it difficult to unify the activity image generated by the three-dimensional Gaussian representation with the PET system matrix, time-of-flight response function, random event correction term and scattering event correction term for projection domain data consistency optimization.

[0010] 3) When directly optimizing three-dimensional Gaussian elements on low-count PET data, noise overfitting, abnormal local activity, and unstable spatial distribution of Gaussian elements are likely to occur; existing anatomical prior constraint methods are also difficult to adaptively control the introduction of prior information based on the local structural consistency between PET images and MRI or CT images.

[0011] Therefore, there is a need to provide a time-of-flight PET reconstruction method based on three-dimensional Gaussian representation, in order to establish the data transfer relationship between three-dimensional Gaussian representation, kernel matrix-guided voxelization, time-of-flight PET forward projection, and projection domain parameter optimization, so as to improve the stability and local structure representation ability of three-dimensional PET activity distribution reconstruction under low count conditions. Summary of the Invention

[0012] The purpose of this invention is to provide a time-of-flight positron emission tomography reconstruction method, system, electronic device, and computer-readable storage medium based on three-dimensional Gaussian representation, in order to solve the technical problems that existing low-dose or low-count PET reconstruction processes are prone to noise amplification, blurred details, lesion boundary distortion, and decreased quantitative accuracy, as well as the lack of a dedicated reconstruction mechanism in existing three-dimensional Gaussian representation methods that combines with time-of-flight PET physical imaging models, Poisson count statistics, and multimodal anatomical priors.

[0013] This invention is achieved through the following technical solution:

[0014] This invention discloses a time-of-flight positron emission tomography reconstruction method based on three-dimensional Gaussian representation, comprising:

[0015] 1) Obtain the measured time-of-flight PET sinusoidal plot, registered MRI and / or CT images, system matrix, time-of-flight response, and correction terms, and obtain the initial PET image from the measured sinusoidal plot; the correction terms are random correction terms and / or scattering correction terms;

[0016] 2) Initialize the position, covariance, and activity intensity of Gaussian elements based on the initial PET image to obtain a three-dimensional Gaussian model;

[0017] 3) Based on the reconstructed mesh of the three-dimensional Gaussian model, extract the local features of the initial PET image and the registered MRI and / or CT images to obtain the kernel matrix;

[0018] 4) Voxelize the three-dimensional Gaussian model based on the kernel matrix to obtain the predicted PET activity image;

[0019] 5) Based on the predicted PET activity image, system matrix, time-of-flight response and correction terms, forward projection is performed to obtain the predicted time-of-flight PET sine curve;

[0020] 6) Construct a Poisson negative log-likelihood loss based on the predicted flight time PET sine plot and the measured flight time PET sine plot. Update the Gaussian parameters based on this loss and clone or split the Gaussian elements to obtain the updated three-dimensional Gaussian model.

[0021] 7) Voxelize the data based on the updated 3D Gaussian model and kernel matrix to obtain the 3D PET reconstructed image.

[0022] As a further improvement, step 2) of the present invention specifically involves: obtaining an initial PET image based on the measured time-of-flight PET sine curve; selecting the initial position of the three-dimensional Gaussian elements and setting the initial activity intensity based on the voxel activity of the initial PET image; and setting the initial covariance parameter based on the voxel spacing.

[0023] As a further improvement, in 2) of the present invention, the position parameter is used to determine the center position of the three-dimensional Gaussian element, the covariance parameter is determined by the scale parameter and the orientation parameter, and is used to determine the anisotropic spatial distribution of the three-dimensional Gaussian element, and the activity intensity parameter is used to determine the activity contribution of the three-dimensional Gaussian element.

[0024] As a further improvement, in step 3) of the present invention, the construction of the kernel matrix includes: acquiring magnetic resonance images and / or computed tomography images registered with PET data as image priors, extracting local features of the initial PET image and image priors, determining the weights between voxels based on the similarity between the local features, and constructing the kernel matrix.

[0025] As a further improvement, in step 4) of the present invention, voxelization includes: calculating the contribution weight of each three-dimensional Gaussian element to each voxel based on its position and covariance parameter, combining the contribution weight with the activity intensity parameter and aggregating the activity contribution of the same voxel, and then using the kernel matrix to map the voxel activity to obtain the predicted PET activity image.

[0026] As a further improvement, the forward projection in step 5) of the present invention includes: calculating the projection contribution of each voxel in the predicted PET activity image to each response line according to the system matrix, allocating the projection contribution to the corresponding time-of-flight bins according to the time-of-flight response function, and adding random correction terms and / or scattering correction terms to obtain the predicted time-of-flight PET sine map.

[0027] As a further improvement, the method of updating the Gaussian parameters based on the loss described in this invention is as follows: constructing a Poisson negative log-likelihood loss based on the predicted time-of-flight (PET) sine curve and the measured time-of-flight (PET) sine curve, updating the position parameters, covariance parameters, and activity intensity parameters of the three-dimensional Gaussian elements based on the loss, and then re-voxelating and forward projecting.

[0028] As a further improvement, the cloning or splitting in step 6) of the present invention includes: during the iterative update process, determining the three-dimensional Gaussian primitives to be adjusted based on the position parameter gradient and spatial scale of the three-dimensional Gaussian primitives, cloning or splitting the three-dimensional Gaussian primitives that meet the preset conditions, and inputting the adjusted three-dimensional Gaussian model into the next voxelization process.

[0029] As a further improvement, when the Poisson negative log-likelihood loss in step 6) satisfies the preset convergence condition or reaches the preset number of iterations, the three-dimensional Gaussian parameters are stopped from being updated, the updated three-dimensional Gaussian model is voxelized, and the three-dimensional PET reconstructed image is obtained and output.

[0030] The present invention also discloses a time-of-flight positron emission tomography reconstruction device based on three-dimensional Gaussian representation, comprising:

[0031] The data and initialization module is used to acquire the measured time-of-flight PET sine plot, system matrix, time-of-flight response and random and / or scattering correction terms, and to obtain the initial PET image from the measured sine plot;

[0032] The Gaussian characterization module is used to initialize the position, covariance, and activity intensity of Gaussian elements based on the initial PET image to obtain a three-dimensional Gaussian model.

[0033] The dissecting kernel prior module is used to extract local features from the initial PET image and the registered MRI and / or CT images to obtain the kernel matrix;

[0034] The voxelization module is used to obtain predicted PET activity images based on a three-dimensional Gaussian model and kernel matrix.

[0035] The forward projection module is used to perform forward projection based on the predicted PET activity image, system matrix, time-of-flight response and correction terms to obtain the predicted time-of-flight PET sine curve;

[0036] The optimization module is used to construct a Poisson negative log-likelihood loss based on the predicted flight time PET sine plot and the measured flight time PET sine plot, update the Gaussian parameters based on the loss, and clone or split the Gaussian elements to obtain the updated three-dimensional Gaussian model.

[0037] The image output module is used to perform voxelization based on the updated 3D Gaussian model and kernel matrix to obtain a 3D PET reconstructed image.

[0038] The beneficial effects of this invention are as follows:

[0039] 1) This invention establishes an explicit three-dimensional Gaussian space representation mechanism for time-of-flight PET reconstruction, which can improve the expressive power of local structures.

[0040] This invention does not use fixed voxel values ​​or global network parameters to directly represent the entire PET activity distribution. Instead, it utilizes multiple three-dimensional Gaussian elements with spatial location, scale, orientation, and activity intensity parameters to locally parameterize different spatial regions. Each three-dimensional Gaussian element can independently adjust its center position, spatial extent, anisotropic direction, and activity contribution according to the structural morphology of its region, thereby more flexibly describing lesion boundaries, fine structures, and activity changes in different directions.

[0041] Compared to fixed reconstruction mesh representation, this approach reduces the impact of local activity variations on global parameters, enhances the expressive power of local high-frequency structures while maintaining background smoothness, and helps alleviate the contradiction between noise suppression and lesion detail restoration under low count conditions. The three-dimensional Gaussian meta-parameters also have clear spatial meanings, facilitating the analysis of activity distribution and model optimization states in different regions, and improving the interpretability of the reconstruction process.

[0042] 2) This invention establishes a complete data transfer path between three-dimensional Gaussian voxelization and time-of-flight PET physical forward model, improving the physical consistency between the reconstruction results and the actual acquired data.

[0043] This invention uses the voxel positions in the PET 3D reconstruction mesh as the generation object, calculates the activity contribution based on the spatial relationship between the 3D Gaussian elements and each voxel, and generates a predicted PET activity image, without relying on the camera perspective and 2D image rendering process in the 3D Gaussian method for natural scenes.

[0044] The generated predicted PET activity image is further combined with the PET system matrix, time-of-flight response function, random event correction term, and scattering event correction term to obtain predicted PET projection data corresponding to different response lines and different time-of-flight bins. Therefore, the update of the three-dimensional Gaussian element parameters is jointly constrained by the actual PET detection geometry, time-of-flight positioning information, and counting statistics, avoiding the inconsistency problem of projection data that may occur when processing only in the image domain.

[0045] By utilizing time-of-flight information to spatially locate radioactive events along the response line, it is possible to narrow down the possible sources of a single coincidence event in the direction of the response line, improve the spatial constraint capability of low-count projection data, and thus improve the localization accuracy and convergence stability of the reconstructed image.

[0046] 3) This invention utilizes the Poisson data consistency of the projection domain to directly optimize three-dimensional Gaussian elements without relying on paired training data, thereby improving the applicability of the method under different acquisition conditions.

[0047] This invention constructs a Poisson negative log-likelihood loss based on predicted time-of-flight PET projection data and measured time-of-flight PET projection data, and updates the position, scale, orientation and activity intensity parameters of the three-dimensional Gaussian elements through this loss, so that the optimization process matches the Poisson statistical characteristics of PET count data.

[0048] This method directly utilizes the measured projection data of the object to be reconstructed for optimization. It does not require the prior collection of a large number of paired low-count PET data and high-quality reference images, nor does it rely on fixed model parameters trained on specific equipment, scanning protocols, or anatomical sites. Therefore, when the PET equipment, scanning protocol, radioactive tracer, acquisition count, or imaging site changes, data consistency constraints can still be re-established based on the projection data of the current object, reducing the impact of differences in training data distribution on the reconstruction results.

[0049] 4) This invention constructs a kernel prior matrix through multimodal local features, which can reduce the introduction of erroneous anatomical structures while suppressing Poisson noise.

[0050] This invention does not directly use MRI or CT images to replace PET structures, nor does it apply the same intensity of anatomical constraints to all regions. Instead, it extracts local features from the initial PET image and the registered MRI and / or CT images, determines the similarity weights between voxels based on the structural similarity of different modalities in the local region, and constructs a kernel prior matrix from the similarity weights.

[0051] In regions where the PET image and the anatomical prior image have the same structure, the nuclear prior can use high-resolution boundary information from MRI or CT images to guide the activity recovery between adjacent or similar voxels. In regions where the structures of different modalities are inconsistent, the local features of the PET image itself can reduce the influence of the anatomical prior and reduce the propagation of non-corresponding structures from MRI or CT to the PET reconstruction results.

[0052] Therefore, this nuclear prior constraint can reduce structural bias caused by directly using anatomical images while suppressing low counting noise, maintaining tissue boundaries and enhancing local structural continuity, which is beneficial to improving the reliability of lesion activity recovery and PET quantitative analysis.

[0053] 5) This invention improves the adaptability of three-dimensional Gaussian representation to different spatial complexities through adaptive cloning and splitting of Gaussian units.

[0054] During the iterative optimization process, this invention selects Gaussian units whose representational power needs to be increased based on the gradient of their positional parameters, spatial scale, or other parameter states, and then clones or splits them. For regions with slow activity changes, fewer Gaussian units with relatively large scales can be used for representation; for lesion boundaries, fine structures, or regions with rapid activity changes, the number of local Gaussian units can be increased by cloning or splitting, while their spatial scale can be reduced.

[0055] Therefore, this invention can allocate more representational power to regions with complex structures or large reconstruction errors, avoiding the uniform placement of a large number of Gaussian elements throughout the reconstruction space. This improves the ability to express details while controlling the number of model parameters and computational overhead. This adaptive control also helps reduce boundary blurring caused by excessively large Gaussian element scales and local structural loss caused by insufficient Gaussian element numbers.

[0056] 6) This invention initializes the three-dimensional Gaussian primitives using the initial PET image, which can reduce the difficulty of solving non-convex optimization and improve reconstruction stability.

[0057] This invention utilizes measured PET projection data to obtain an initial PET image, and sets the initial spatial position and activity intensity of the three-dimensional Gaussian elements based on the voxel positions and activity distribution in the initial PET image, so that the three-dimensional Gaussian elements are distributed in regions with actual radioactivity at the start of optimization.

[0058] Compared to randomly setting 3D Gaussian elements, this initialization method can reduce the occurrence of a large number of Gaussian elements clustering in inactive regions or deviating from the target structure, shorten the optimization process required for Gaussian elements to move to reasonable spatial positions, and reduce the possibility of the model getting trapped in unreasonable local optima, spatial distribution instability, or morphological collapse, thereby improving the convergence speed and repeatability of low-count PET reconstruction.

[0059] 7) This invention can improve the quality of reconstructed images, lesion visibility, and quantitative stability under low count conditions.

[0060] In the simulated PET data test of the embodiment, at count levels of 108×10^8×10^8, 5×10^75×10^7, 107×10^7×10^7, and 5×10^65×10^65×10^6, the peak signal-to-noise ratios obtained by the method of the present invention with the introduction of kernel prior were 26.29 dB, 25.72 dB, 24.20 dB, and 23.43 dB, respectively, and the structural similarities were 0.9423, 0.9326, 0.8956, and 0.8633, respectively.

[0061] Under a count of 10^7 × 10^7 × 10^7, the method of this invention improves the peak signal-to-noise ratio by approximately 1.11 dB and the structural similarity by approximately 0.0395 compared to the implicit neural representation method; under a count of 5 × 10^65 × 10^65, the peak signal-to-noise ratio is improved by approximately 4.54 dB and the structural similarity by approximately 0.1341 compared to the maximum likelihood expectation maximization reconstruction method.

[0062] In the clinical data examples, the lesion contrast-to-noise ratio of the reconstructed image after introducing the kernel prior reached 9.25, which is higher than 9.00 without introducing the kernel prior and 7.39 of the maximum likelihood expectation maximization reconstruction method. This shows that the present invention can maintain lesion activity and boundary information while suppressing background noise.

[0063] The above data are test results under specific embodiments, illustrating the synergistic effect between 3D Gaussian local representation, time-of-flight PET physical constraints, and multimodal kernel priors, which can improve the noise-resolution tradeoff in low-count PET reconstruction.

[0064] 8) This invention forms a complete PET reconstruction process that can be executed by computer equipment, and has good engineering implementation and expansion value.

[0065] This invention organizes data acquisition, 3D Gaussian representation, kernel prior construction, 3D voxelization, time-of-flight forward projection, Poisson data consistency optimization, adaptive control, and image output into an interconnected data processing flow. The input and output relationships of each step are clear and can be executed by a processor, graphics processor, or other computing device.

[0066] This invention can be developed into a standalone PET image reconstruction program or integrated into PET scanning equipment, medical image processing workstations, or remote reconstruction platforms. It can also be extended to PET reconstruction of the brain, chest, tumors, and whole body, as well as PET acquisition conditions with different counting levels and different time-of-flight resolutions. Attached Figure Description

[0067] Figure 1 This is a schematic diagram of the overall process of the time-of-flight positron emission tomography reconstruction method based on three-dimensional Gaussian representation and kernel prior modeling, according to an embodiment of the present invention.

[0068] Figure 2 This is a comparison chart of reconstruction results on simulated PET data of the brain at different counting levels, according to an embodiment of the present invention.

[0069] Figure 3 This is a comparison chart of quantitative evaluation indicators at different counting levels in embodiments of the present invention.

[0070] Figure 4 This is a comparison chart of reconstruction results based on real clinical PET data in the embodiments of the present invention. Detailed Implementation

[0071] This invention discloses a time-of-flight positron emission tomography reconstruction method based on three-dimensional Gaussian representation, comprising:

[0072] 1) Obtain the measured time-of-flight PET sinusoidal plot, registered MRI and / or CT images, system matrix, time-of-flight response, and correction terms, and obtain the initial PET image from the measured sinusoidal plot; the correction terms are random correction terms and / or scattering correction terms;

[0073] 2) Initialize the position, covariance, and activity intensity of Gaussian elements based on the initial PET image to obtain a three-dimensional Gaussian model. Obtain the initial PET image from the measured time-of-flight PET sine curve. Select the initial position of the three-dimensional Gaussian elements and set the initial activity intensity based on the voxel activity of the initial PET image. Set the initial covariance parameter based on the voxel spacing. The position parameter is used to determine the center position of the three-dimensional Gaussian elements. The covariance parameter is determined by the scale and orientation parameters and is used to determine the anisotropic spatial distribution of the three-dimensional Gaussian elements. The activity intensity parameter is used to determine the activity contribution of the three-dimensional Gaussian elements.

[0074] 3) Based on the reconstructed mesh of the three-dimensional Gaussian model, extract local features from the initial PET image and the registered MRI and / or CT images to obtain the kernel matrix; the construction of the kernel matrix includes: obtaining the MRI and / or computed tomography images registered with the PET data as image priors, extracting local features from the initial PET image and the image priors, determining the voxel weights based on the similarity between the local features, and constructing the kernel matrix.

[0075] 4) Voxelize the three-dimensional Gaussian model according to the kernel matrix to obtain the predicted PET activity image; Voxelization includes: calculating the contribution weight of each three-dimensional Gaussian element to each voxel based on its position and covariance parameter, combining the contribution weight with the activity intensity parameter and aggregating the activity contribution of the same voxel, and then using the kernel matrix to map the voxel activity to obtain the predicted PET activity image.

[0076] 5) Forward projection is performed based on the predicted PET activity image, system matrix, time-of-flight response and correction terms to obtain the predicted time-of-flight PET sine curve. Forward projection includes: calculating the projection contribution of each voxel in the predicted PET activity image to each response line based on the system matrix, allocating the projection contribution to the corresponding time-of-flight bins based on the time-of-flight response function, and adding random correction terms and / or scattering correction terms to obtain the predicted time-of-flight PET sine curve.

[0077] 6) Construct a Poisson negative log-likelihood loss based on the predicted and measured time-of-flight (TOF) PET sine maps. Update Gaussian trigonometric parameters using this loss and clone or split Gaussian trigonometric units to obtain an updated 3D Gaussian model. Cloning or splitting includes: during the iterative update process, determining the 3D Gaussian trigonometric units to be adjusted based on their position parameter gradients and spatial scale; cloning or splitting 3D Gaussian trigonometric units that meet preset conditions; and inputting the adjusted 3D Gaussian model into the next voxelization process. When the Poisson negative log-likelihood loss meets the preset convergence condition or reaches the preset number of iterations, stop updating the 3D Gaussian parameters, voxelize the updated 3D Gaussian model, and obtain and output the 3D PET reconstructed image. Specifically, updating the Gaussian trigonometric parameters using this loss involves: constructing a Poisson negative log-likelihood loss based on the predicted and measured TOF PET sine maps; updating the position parameters, covariance parameters, and activity intensity parameters of the 3D Gaussian trigonometric units based on the loss; and re-voxelizing and forward projection.

[0078] 7) Voxelize the data based on the updated 3D Gaussian model and kernel matrix to obtain the 3D PET reconstructed image.

[0079] The present invention also discloses a time-of-flight positron emission tomography reconstruction device based on three-dimensional Gaussian representation, comprising:

[0080] The data and initialization module is used to acquire the measured time-of-flight PET sine plot, system matrix, time-of-flight response and random and / or scattering correction terms, and to obtain the initial PET image from the measured sine plot;

[0081] The Gaussian characterization module is used to initialize the position, covariance, and activity intensity of Gaussian elements based on the initial PET image to obtain a three-dimensional Gaussian model.

[0082] The dissecting kernel prior module is used to extract local features from the initial PET image and the registered MRI and / or CT images to obtain the kernel matrix;

[0083] The voxelization module is used to obtain predicted PET activity images based on a three-dimensional Gaussian model and kernel matrix.

[0084] The forward projection module is used to perform forward projection based on the predicted PET activity image, system matrix, time-of-flight response and correction terms to obtain the predicted time-of-flight PET sine curve;

[0085] The optimization module is used to construct a Poisson negative log-likelihood loss based on the predicted flight time PET sine plot and the measured flight time PET sine plot, update the Gaussian parameters based on the loss, and clone or split the Gaussian elements to obtain the updated three-dimensional Gaussian model.

[0086] The image output module is used to perform voxelization based on the updated 3D Gaussian model and kernel matrix to obtain a 3D PET reconstructed image.

[0087] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be noted that the following embodiments are used to illustrate the present invention, and not to limit the scope of protection of the present invention.

[0088] Brain time-of-flight PET image reconstruction:

[0089] (1) Acquire data and establish a three-dimensional reconstruction space

[0090] like Figure 1 As shown, the measured time-of-flight PET sine curve, PET system matrix, time-of-flight response function, and correction terms for random events and / or scattering events of the object to be reconstructed are first obtained.

[0091] This embodiment uses BrainWeb digital brain phantoms to generate three-dimensional PET activity images of fluorodeoxyglucose and their corresponding magnetic resonance images. The PET image size is set to 128×128×96, and the voxel size is set to 2 mm×2 mm×2 mm. Eight lesions with radii ranging from 2 to 8 mm are randomly placed in the brain phantom. The time-of-flight resolution is set to 200 ps, ​​and the PET system matrix is ​​calculated using the Joseph3D projection algorithm in PyTomography software, generating PET projection data with a size of 224×449×4096.

[0092] The total count in the projected data was set to 1×10^8, 5×10^7, 1×10^7, and 5×10^6, respectively, to simulate different low count levels. For projected data that did not additionally simulate random events and scattering events, the random event correction term and the scattering event correction term were set to 0; for projected data containing random events or scattering events, the corresponding random event estimates and scattering event estimates were used as additive correction terms in the forward projection.

[0093] A 128×128×96 three-dimensional reconstruction mesh was constructed based on the size and voxel spacing of the target PET image, and the center coordinates of each voxel in the three-dimensional reconstruction mesh were calculated. The simulation data size, lesion settings, time-of-flight resolution, and system matrix calculation method are all consistent with the existing experimental settings.

[0094] (2) Obtain the initial PET image and initialize the three-dimensional Gaussian unit.

[0095] Initial PET reconstruction is performed based on the measured time-of-flight PET sine curve. This embodiment uses the ordered subset expectation-maximization method to obtain the initial PET image. The initial PET image is normalized to 0-1, and three-dimensional Gaussian units are initialized based on the voxel activity distribution in the initial PET image. Specifically, voxels with normalized activity values ​​not lower than 0.005 are selected as candidate voxels, and the sampling probability is determined according to the proportion of the candidate voxel activity values. Approximately 80,000 positions are sampled from the candidate voxels as the initial center positions of the three-dimensional Gaussian units.

[0096] Each 3D Gaussian element includes spatial position parameters, scale parameters, orientation parameters, and activity intensity parameters. Among them:

[0097] The spatial position parameter is set to the center coordinates of the sampled voxel; the initial scale parameter is set according to a voxel spacing of 2 mm; the initial orientation parameter is set to unit rotation; and the initial activity intensity parameter is set to the product of the corresponding voxel activity value and the initial scaling factor. In one specific embodiment, the initial scaling factor is set to 0.50.

[0098] The initial three-dimensional Gaussian model is constructed from the three-dimensional Gaussian elements initialized above. Using the initial PET image for parameter initialization ensures that the three-dimensional Gaussian elements are preferentially distributed in regions with radioactivity, reducing invalid Gaussian elements generated by random initialization.

[0099] (3) Construct a three-dimensional Gaussian space representation model

[0100] Let the number of three-dimensional Gaussian elements be . , No. Each three-dimensional Gaussian element is characterized by its central location, covariance matrix, and activity intensity parameter.

[0101] The center position is used to determine the spatial position of the three-dimensional Gaussian element in the PET image coordinate system; the covariance matrix is ​​determined by the scale and orientation parameters in three spatial directions, and is used to describe the spatial extension range and anisotropic direction of the three-dimensional Gaussian element; the activity intensity parameter is constrained to a non-negative value, and is used to describe the radioactivity contribution of the three-dimensional Gaussian element.

[0102] For any voxel location in the 3D reconstructed mesh, calculate the covariance-weighted distance between the center location of each 3D Gaussian element and the center location of the voxel. Based on the distance, obtain the contribution weight of each 3D Gaussian element to the voxel, and multiply the contribution weight by the corresponding activity intensity parameter to obtain the activity contribution of each 3D Gaussian element to the voxel.

[0103] In the above manner, the three-dimensional PET activity distribution to be reconstructed is represented as a combination of multiple independently optimizable anisotropic three-dimensional Gaussian elements.

[0104] (4) Construct the multimodal kernel prior matrix

[0105] A magnetic resonance image spatially registered with the initial PET image was acquired, and the magnetic resonance image was resampled to 128×128×96 to ensure that its voxel coordinates correspond one-to-one with the PET 3D reconstruction mesh. The intensity of the initial PET image and the magnetic resonance image were normalized respectively, and the image intensity was converted to 0 to 1.

[0106] For each voxel, its local functional features in the initial PET image and its local anatomical features in the magnetic resonance image are extracted respectively.

[0107] The local structural similarity between the initial PET image and the magnetic resonance image within the corresponding voxel neighborhood is calculated, and voxel-level reliability weights are determined based on the local structural similarity. In one specific embodiment, the structural similarity threshold is set to 0.60; when the local structural similarity is higher than the threshold, the contribution of magnetic resonance anatomical features to voxel similarity is increased; when the local structural similarity is lower than the threshold, the contribution of PET functional features themselves is increased.

[0108] Based on the PET local feature distance, the magnetic resonance local feature distance, and the voxel-level reliability weight, the similarity weight between each voxel and its nearest neighbor voxels is calculated. The similarity weights are then written into a sparse matrix, and each row of the sparse matrix is ​​normalized to obtain the kernel matrix. .

[0109] Each row in the kernel matrix represents the association between a target voxel and several similar voxels, which is used to fuse PET functional information and magnetic resonance anatomy information in the subsequent voxelization process.

[0110] (5) Perform three-dimensional Gaussian voxelization

[0111] The 3D Gaussian model is input into the 3D Gaussian voxelization module. For each voxel in the 3D reconstructed mesh, the following processing is performed:

[0112] First, based on the center position, scale parameter, and orientation parameter of the 3D Gaussian element, the spatial distribution of the 3D Gaussian element in the 3D reconstruction mesh is calculated. Second, the contribution weight of the 3D Gaussian element to the target voxel is calculated. Third, the contribution weight is multiplied by the activity intensity parameter of the 3D Gaussian element to obtain the activity contribution of the 3D Gaussian element to the target voxel. Finally, the activity contributions of all 3D Gaussian elements acting on the same voxel are summed to obtain the basic predicted activity value of the voxel.

[0113] After performing the above processing on all voxels in the 3D reconstructed mesh, the basic predicted PET activity image x(Θ) is obtained, where Θ represents all 3D Gaussian primitive parameters.

[0114] The kernel matrix obtained in step (4) is used to map the basic predicted PET activity image to obtain the predicted PET activity image after kernel prior constraint:

[0115]

[0116] in, This is used as input to the time-of-flight PET forward projection model. This processing establishes correlations between structurally similar voxels while avoiding the direct substitution of PET activity values ​​with magnetic resonance image intensity.

[0117] (6) Perform time-of-flight PET forward projection

[0118] The predicted PET activity image with nuclear prior constraints is input into the time-of-flight PET forward projection model.

[0119] For the m-th response line, firstly, the spatial projection contribution of each voxel in the predicted PET activity image to the response line is calculated based on the PET system matrix; then, the expected photon arrival time difference corresponding to the voxel is calculated based on the spatial position of the voxel in the direction of the response line; next, the spatial projection contribution of the voxel is allocated to one or more corresponding time-of-flight bins according to the time-of-flight response function; finally, the voxel contributions allocated to the same response line and the same time-of-flight bin are summed, and random event correction terms and / or scattering event correction terms are added to obtain the predicted time-of-flight PET sine curve.

[0120] Each value in the predicted time-of-flight PET sine curve corresponds to a response line and a time-of-flight bin. The PET system matrix includes the detector geometric response, the projection relationship between voxels and response lines, attenuation correction, and normalization correction; the time-of-flight response function adopts a one-dimensional Gaussian response function corresponding to a 200 ps time-of-flight resolution.

[0121] (7) Construct the loss function and update the three-dimensional Gaussian parameters

[0122] The predicted flight time PET sine plot and the measured flight time PET sine plot are input into the parameter optimization module, and a Poisson negative log-likelihood data consistency term is constructed based on the two. For the measured counts... Predicted count is The projection position corresponds to the loss, which is the predicted count minus the product of the measured count and the logarithm of the predicted count.

[0123] Simultaneously, a three-dimensional total variational regularization term is calculated for the predicted PET activity images after kernel prior constraints. The final optimization objective is composed of a weighted average of the Poisson negative log-likelihood data consistency term and the three-dimensional total variational regularization term.

[0124] In a preferred embodiment, the regularization weight is set to 0.01. Parameter sensitivity verification also tested the reconstruction performance with regularization weights of 0.01, 0.05, 0.10, and 0.50, respectively.

[0125] This embodiment uses the Adam optimizer with a base learning rate of 5 × 10^-4. The learning rates for the position parameters, scale parameters, orientation parameters, and activity intensity parameters of the 3D Gaussian primitives are set to 0.005, 0.01, 0.001, and 0.005, respectively. The reconstruction program is implemented in PyTorch and runs on an NVIDIA V100 graphics processor with 32 GB of video memory.

[0126] After each parameter update, the updated 3D Gaussian model is re-input into the 3D Gaussian voxelization module and the time-of-flight PET forward projection module, and the predicted PET activity image and the predicted time-of-flight PET sine curve are regenerated in sequence.

[0127] (8) Perform three-dimensional Gaussian element adaptive control

[0128] During the parameter iterative update process, the position parameter gradient and spatial scale of each 3D Gaussian element are calculated.

[0129] When the gradient of the position parameter of a three-dimensional Gaussian element is greater than the cloning threshold and the spatial scale is less than the scale threshold, the three-dimensional Gaussian element is cloned; the cloned three-dimensional Gaussian element inherits the scale, orientation and activity intensity of the original Gaussian element, and a small spatial offset is applied to its center position.

[0130] When the gradient of the position parameter of the three-dimensional Gaussian element is greater than the splitting threshold and the spatial scale is not less than the scale threshold, the three-dimensional Gaussian element is split into multiple three-dimensional Gaussian elements with smaller scales, and the split three-dimensional Gaussian elements are set within the spatial range covered by the original three-dimensional Gaussian element.

[0131] The cloned or split 3D Gaussian model is input into the next 3D Gaussian voxelization and time-of-flight PET forward projection process to increase the local representation capability of lesion boundaries and complex structural regions.

[0132] (9) Output three-dimensional PET reconstructed images

[0133] When the preset number of iterations is reached or the Poisson negative log-likelihood loss meets the preset convergence condition, the updating of the three-dimensional Gaussian meta-parameters is stopped.

[0134] The final updated 3D Gaussian model is input into the 3D Gaussian voxelization module to calculate the activity contribution of each 3D Gaussian voxel to each voxel in the 128×128×96 3D reconstruction mesh. The activity contributions of the same voxel are aggregated and mapped using the kernel matrix to obtain the final 3D PET reconstruction image.

[0135] The final reconstructed image has a voxel size of 2 mm × 2 mm × 2 mm, consistent with the simulated ground truth image and the registered magnetic resonance image.

[0136] The present invention also discloses a time-of-flight positron emission tomography reconstruction device based on three-dimensional Gaussian representation, comprising:

[0137] The data and initialization module is used to acquire the measured time-of-flight PET sine plot, system matrix, time-of-flight response and random and / or scattering correction terms, and to obtain the initial PET image from the measured sine plot;

[0138] The Gaussian characterization module is used to initialize the position, covariance, and activity intensity of Gaussian elements based on the initial PET image to obtain a three-dimensional Gaussian model.

[0139] The dissecting kernel prior module is used to extract local features from the initial PET image and the registered MRI and / or CT images to obtain the kernel matrix;

[0140] The voxelization module is used to obtain predicted PET activity images based on a three-dimensional Gaussian model and kernel matrix.

[0141] The forward projection module is used to perform forward projection based on the predicted PET activity image, system matrix, time-of-flight response and correction terms to obtain the predicted time-of-flight PET sine curve;

[0142] The optimization module is used to construct a Poisson negative log-likelihood loss based on the predicted flight time PET sine plot and the measured flight time PET sine plot, update the Gaussian parameters based on the loss, and clone or split the Gaussian elements to obtain the updated three-dimensional Gaussian model.

[0143] The image output module is used to perform voxelization based on the updated 3D Gaussian model and kernel matrix to obtain a 3D PET reconstructed image.

[0144] Overall comparison experiment of simulated data:

[0145] To verify the reconstruction performance of the present invention at different counting levels, the following methods were compared: maximum likelihood expectation maximization reconstruction, depth image prior reconstruction, implicit neural representation reconstruction, kernel-free time-of-flight 3D Gaussian reconstruction, and kernel-containing time-of-flight 3D Gaussian reconstruction.

[0146] Aside from the reconstruction methods themselves, all methods used the same simulated activity images, system matrix, time-of-flight resolution, and projection count level. Peak signal-to-noise ratio (PSNR) and structural similarity were used to evaluate overall image quality, while contrast recovery coefficient, background standard deviation, contrast-to-noise ratio (CNR), and maximum standardized uptake were used to evaluate lesion recovery and quantitative stability.

[0147] The experimental results are as follows:

[0148] Table 1. Comparison of reconstruction results at different noise levels in the simulation experiment.

[0149]

[0150] Under a count of 5×10^6, the peak signal-to-noise ratio of the method of this invention with kernel prior is 23.43 dB, which is 4.54 dB higher than the 18.89 dB of the maximum likelihood expectation maximization method; the structural similarity is improved from 0.7292 to 0.8633, an absolute improvement of 0.1341.

[0151] Under a counting condition of 1×10^7, the peak signal-to-noise ratio of the method of the present invention with nuclear prior is 24.20 dB, which is 1.11 dB higher than that of the implicit neural representation method; the structural similarity is improved from 0.8561 to 0.8956, an absolute improvement of 0.0395.

[0152] Figure 2 This is a comparison of reconstruction results on simulated PET data of the brain at different counting levels, according to embodiments of the present invention. The results include simulated ground truth images, maximum likelihood expectation maximization reconstruction, depth image prior reconstruction, implicit neural representation reconstruction, nucleus-free time-of-flight three-dimensional Gaussian reconstruction, and nucleus-based time-of-flight three-dimensional Gaussian reconstruction. Figure 2 As shown, the small red box marks the area where the simulated lesion is located, and the local image next to it is a magnified result of the corresponding lesion area. As the count decreases, the background noise in the maximum likelihood expectation maximization reconstruction increases, and the boundaries of some lesions become blurred in the depth image prior and implicit neural representation results; the method of the present invention with nucleus prior maintains a relatively complete lesion morphology under the same counting conditions.

[0153] Figure 3 This is a comparison chart of quantitative evaluation indicators at different counting levels according to embodiments of the present invention, wherein, Figure 3 (a) in the figure shows the relationship between the contrast recovery coefficient and the background standard deviation. Figure 3 (b) in the figure shows the trend of the normalized contrast recovery coefficient. Figure 3 (e) in the figure shows the trend of the contrast-to-noise ratio. Figure 3 (d) in the graph represents the stability change of the maximum standard intake value. For example... Figure 3As shown, the relationship between contrast recovery coefficient and background standard deviation, normalized contrast recovery coefficient, contrast-to-noise ratio, and stability of maximum standard uptake value were compared for different methods to evaluate lesion contrast recovery, background noise, and quantitative stability.

[0154] Nuclear prior univariate comparison experiment:

[0155] To clarify the causal relationship between kernel prior technical features and reconstruction results, a univariate comparative experiment was set up. The experimental group enabled kernel matrix mapping, while the control group disabled kernel matrix mapping. All other data, 3D Gaussian initialization, forward projection model, optimizer, learning rate, and iteration settings remained consistent.

[0156] The experimental results are as follows:

[0157] Table 2 Comparison of evaluation indicators and their improvement values ​​after adding nuclear priors

[0158]

[0159] Under the 1×10^7 counting condition, adding only the kernel prior improves the peak signal-to-noise ratio by 0.72 dB and the structural similarity by 0.0289, representing improvements of approximately 3.07% and 3.33% respectively compared to the result without the kernel prior. This indicates that, when the 3D Gaussian representation, initialization method, and projection domain optimization conditions remain unchanged, kernel matrix mapping can improve the structural consistency and low counting stability of the reconstructed image.

[0160] Univariate sensitivity experiment of parameters:

[0161] Under the condition of keeping the same data and other parameters unchanged, change the regularization weight and the initial scaling factor respectively.

[0162] When the regularization weights in the kernel-based prior method are set to 0.01, 0.05, 0.10, and 0.50, the peak signal-to-noise ratios (PSNRs) are 25.57 dB, 25.52 dB, 25.38 dB, and 23.91 dB, respectively, and the structural similarities are 0.9519, 0.9510, 0.9489, and 0.9259, respectively. Increasing the regularization weights from 0.01 to 0.50 reduces the PSNR by 1.66 dB and the structural similarity by 0.0260, indicating that excessively large regularization weights may cause over-smoothing.

[0163] When the initial scaling factor was set to 0.20, 0.50, and 0.80, the peak signal-to-noise ratio (PSNR) of the kernel-based prior method was 24.69 dB, 25.52 dB, and 25.57 dB, respectively, and the structural similarities were 0.9402, 0.9513, and 0.9519, respectively. Increasing the initial scaling factor from 0.20 to 0.80 improved the PSNR by 0.88 dB and the structural similarity by 0.0117. These parameter sensitivity data are consistent with the ablation results in previous experiments.

[0164] Real-world clinical PET / CT reconstruction

[0165] The invention was validated using clinical whole-body fluorodeoxyglucose time-of-flight PET / CT data. The original PET image voxel size was 2.1 mm × 2.1 mm × 2.1 mm, and the original CT image voxel size was 0.875 mm × 0.875 mm × 1.5 mm. The PET and CT images were spatially registered and then cropped or resampled to 128 × 128 × 96.

[0166] CT images were used as anatomical prior images, and a kernel matrix was constructed according to the method described in Example 1. Clinical PET reconstructed images were obtained using the same three-dimensional Gaussian voxelization, time-of-flight forward projection, and Poisson negative log-likelihood optimization process. The clinical data preprocessing size and voxel settings were consistent with existing experiments.

[0167] Figure 4 This is a comparison of reconstruction results on real clinical PET data according to embodiments of the present invention, including a reference image, maximum likelihood expectation maximization reconstruction, depth image prior reconstruction, implicit neural representation reconstruction, nucleus-prior time-of-flight 3D Gaussian reconstruction, and nucleus-prior time-of-flight 3D Gaussian reconstruction results; small red boxes indicate the lesion area, and images within large red boxes represent local magnification of the corresponding lesion area. The contrast-to-noise ratios of the lesions using different methods are as follows:

[0168] The maximum likelihood expectation maximization method is 7.39, the depth image prior method is 7.67, the implicit neural representation method is 8.57, the method of the present invention without kernel prior is 9.00, and the method of the present invention with kernel prior is 9.25.

[0169] With only the kernel prior enabled or disabled, the contrast-to-noise ratio improved from 9.00 to 9.25, an absolute improvement of 0.25 and a relative improvement of approximately 2.78%. Compared with the maximum likelihood expectation maximization method, the contrast-to-noise ratio improved by 1.86 and the relative improvement by approximately 25.17%. These results indicate that combining the kernel prior with three-dimensional Gaussian representation can improve the distinguishability of clinical lesion regions relative to the background.

[0170] The above description of the embodiments is provided to enable those skilled in the art to understand and apply the present invention. Those skilled in the art can readily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made to the present invention by those skilled in the art based on the disclosure thereof should be within the scope of protection of the present invention.

Claims

1. A time-of-flight positron emission tomography reconstruction method based on three-dimensional Gaussian representation, characterized in that, include: 1) Obtain the measured time-of-flight PET sinusoidal plot, registered MRI and / or CT images, system matrix, time-of-flight response, and correction terms, and obtain the initial PET image from the measured time-of-flight PET sinusoidal plot; the correction terms are random correction terms and / or scattering correction terms; 2) Initialize the position, covariance, and activity intensity of Gaussian elements based on the initial PET image to obtain a three-dimensional Gaussian model; 3) Based on the reconstructed mesh of the three-dimensional Gaussian model, extract the local features of the initial PET image and the registered MRI and / or CT images to obtain the kernel matrix; 4) Voxelize the three-dimensional Gaussian model according to the kernel matrix to obtain the predicted PET activity image; the voxelization includes: calculating the contribution weight of each three-dimensional Gaussian element to each voxel according to the position and covariance parameter, combining the contribution weight with the activity intensity parameter and aggregating the activity contribution of the same voxel, and then using the kernel matrix to map the voxel activity to obtain the predicted PET activity image. 5) Based on the predicted PET activity image, system matrix, time-of-flight response and correction terms, forward projection is performed to obtain the predicted time-of-flight PET sine curve; 6) Construct a Poisson negative log-likelihood loss based on the predicted flight time PET sine plot and the measured flight time PET sine plot. Update the Gaussian parameters based on this loss and clone or split the Gaussian elements to obtain the updated three-dimensional Gaussian model. 7) Voxelize the data based on the updated 3D Gaussian model and kernel matrix to obtain the 3D PET reconstructed image.

2. The method according to claim 1, characterized in that, Specifically, step 2) involves obtaining an initial PET image based on the measured time-of-flight PET sine curve, selecting the initial position of the three-dimensional Gaussian elements and setting the initial activity intensity based on the voxel activity of the initial PET image, and setting the initial covariance parameter based on the voxel spacing.

3. The method according to claim 2, characterized in that, In step 2), the position parameter is used to determine the center position of the three-dimensional Gaussian element, the covariance parameter is determined by the scale parameter and the orientation parameter, and is used to determine the anisotropic spatial distribution of the three-dimensional Gaussian element, and the activity intensity parameter is used to determine the activity contribution of the three-dimensional Gaussian element.

4. The method according to claim 1, 2, or 3, characterized in that, In step 3), the construction of the kernel matrix includes: acquiring magnetic resonance images and / or computed tomography images registered with PET data as image priors, extracting local features of the initial PET image and image priors, determining the weights between voxels based on the similarity between local features, and constructing the kernel matrix.

5. The method according to claim 4, characterized in that, The forward projection in step 5) includes: calculating the projection contribution of each voxel in the predicted PET activity image to each response line according to the system matrix, allocating the projection contribution to the corresponding time-of-flight bins according to the time-of-flight response function, and adding random correction terms and / or scattering correction terms to obtain the predicted time-of-flight PET sine curve.

6. The method according to claim 5, characterized in that, The method of updating the Gaussian parameters based on the loss is as follows: construct a Poisson negative log-likelihood loss based on the predicted time-of-flight PET sine plot and the measured time-of-flight PET sine plot, update the position parameters, covariance parameters and activity intensity parameters of the three-dimensional Gaussian elements based on the loss, and then re-voxelize and forward project them.

7. The method according to claim 1, 2, 3, 5, or 6, characterized in that, The cloning or splitting in 6) includes: during the iterative update process, determining the three-dimensional Gaussian primitives to be adjusted based on the position parameter gradient and spatial scale of the three-dimensional Gaussian primitives, cloning or splitting the three-dimensional Gaussian primitives that meet the preset conditions, and inputting the adjusted three-dimensional Gaussian model into the next voxelization process.

8. The method according to claim 7, characterized in that, When the Poisson negative log-likelihood loss in step 6) satisfies the preset convergence condition or reaches the preset number of iterations, the update of the three-dimensional Gaussian parameters is stopped, the updated three-dimensional Gaussian model is voxelized, and the three-dimensional PET reconstructed image is obtained and output.

9. A time-of-flight positron emission tomography reconstruction device based on three-dimensional Gaussian representation, characterized in that, include: The data and initialization module is used to acquire the measured time-of-flight PET sinusoidal plot, system matrix, time-of-flight response and random and / or scattering correction terms, and to obtain the initial PET image from the measured time-of-flight PET sinusoidal plot; The Gaussian characterization module is used to initialize the position, covariance, and activity intensity of Gaussian elements based on the initial PET image to obtain a three-dimensional Gaussian model. The dissecting kernel prior module is used to extract local features from the initial PET image and the registered MRI and / or CT images to obtain the kernel matrix; The voxelization module is used to obtain a predicted PET activity image based on a three-dimensional Gaussian model and a kernel matrix. The voxelization includes: calculating the contribution weight of each three-dimensional Gaussian element to each voxel based on its position and covariance parameter; combining the contribution weight with the activity intensity parameter and aggregating the activity contribution of the same voxel; and then using the kernel matrix to map the voxel activity to obtain a predicted PET activity image. The forward projection module is used to perform forward projection based on the predicted PET activity image, system matrix, time-of-flight response and correction terms to obtain the predicted time-of-flight PET sine curve; The optimization module is used to construct a Poisson negative log-likelihood loss based on the predicted flight time PET sine plot and the measured flight time PET sine plot, update the Gaussian parameters based on the loss, and clone or split the Gaussian elements to obtain the updated three-dimensional Gaussian model. The image output module is used to perform voxelization based on the updated 3D Gaussian model and kernel matrix to obtain a 3D PET reconstructed image.

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