PET / CT (positron emission tomography / computed tomography) image breathing motion artifact correction method based on triple subgroup convolutional network

Abstract

The invention relates to a PET / CT (positron emission tomography / computed tomography) image breathing motion artifact correction method based on a triple subgroup convolutional network, and belongs to the field of nuclear medicine imaging. The invention provides a lightweight triple-subgroup convolution kernel, and the convolution kernel focuses on analyzing the rotation and translation characteristics of coronal planes, sagittal planes and cross sections closely related to PET / CT images so as to realize efficient detail analysis under the condition of clinical small samples. And then, a Transform-subgroup convolution fusion encoder and a pyramid network are constructed in combination, a constructed triple subgroup convolution registration network can combine sub-deformation fields of multiple dimensions to obtain a smooth deformation field, and the deformation field is used for spatial distortion transformation to achieve the purpose of artifact correction. According to the method, artifact correction experiment comparison is carried out by using pixel body membrane simulation data and clinical data, the superiority of the method in the aspects of robustness and generalization ability is proved, and the quality of PET / CT images is effectively improved.

Description

Technical Field

[0001] This invention relates to a method for correcting respiratory motion artifacts in PET / CT images based on triple subgroup convolutional networks, belonging to the field of nuclear medicine imaging technology. Background Technology

[0002] PET / CT imaging technology is of great value in tumor diagnosis, staging, and radiotherapy target delineation because it can provide integrated information on function and anatomy. However, due to the long acquisition time of PET data, respiratory movements of thoracic and abdominal organs can produce severe motion artifacts in the images, leading to blurred images and distorted lesion contours, directly affecting the accuracy of diagnosis and the effectiveness of treatment planning. Currently, respiratory gating technology is often used in clinical practice to reduce these artifacts, but this method relies on external monitoring equipment and has problems such as high hardware costs, strict requirements for patient cooperation, and low data utilization.

[0003] In recent years, deep learning-based deformable image registration methods have provided new approaches for correcting respiratory motion artifacts. However, conventional CNN models struggle to fully capture the unique spatial characteristics of organ motion (such as rotational symmetry) when dealing with non-rigid deformations like lung respiration, and they are highly dependent on large-scale labeled data, resulting in high training costs. Furthermore, the varying displacement amplitudes of different lung organs during respiration can lead to differentiated movement of lesions in different lung regions. Triple subgroup convolution, focusing on the coronal, sagittal, and transverse planes respectively, decomposes complex three-dimensional respiratory motion into orthogonal two-dimensional planes for feature learning, thereby achieving high-precision analysis of organ and tumor dynamics with low computational overhead under small clinical sample conditions. Summary of the Invention

[0004] The technical problem to be solved by this invention is that it provides a method for correcting respiratory motion artifacts in PET / CT images based on triple subgroup convolutional networks, which can be used to solve the problem of respiratory motion artifacts in PET / CT images in the case of small clinical samples. This invention improves the imaging quality and the accuracy of auxiliary treatment planning.

[0005] The technical solution of this invention is: a method for correcting respiratory motion artifacts in PET / CT images based on triple subgroup convolutional networks, the method comprising:

[0006] Step 1: First, define a new triple subgroup convolution kernel. The triple subgroup convolution kernel specializes in the rotational motion features of the coronal, sagittal, and transverse planes to achieve hierarchical analysis of three-dimensional PET / CT images.

[0007] Step 2: Construct a triple subgroup convolutional pyramid registration network by combining the Transformer-subgroup convolutional fusion encoder to achieve the fusion of multi-dimensional sub-deformation fields into the final deformation field;

[0008] Step 3: Use the STN network to distort the final deformation field to achieve artifact correction.

[0009] Step 4: Calculate the similarity between the registered image and the fixed image using a loss function.

[0010] Further, Step 1 includes:

[0011] Step 1.1: Define Lie groups and group convolution;

[0012] Step 1.2: Based on the meaning of Lie groups and group convolution, select SE(3) group as the unit element to construct a triple subgroup convolution kernel. Its rotation axes (x, y, z) correspond to the coronal plane, sagittal plane and transverse plane respectively. Each rotation axis corresponds to four subgroups, and each group of four subgroups is a combination. Each subgroup independently performs isovariant convolution operation under the corresponding rotation transformation.

[0013] Step 1.3: Fix the image and moving images The images are input into a Transformer-subgroup convolutional fusion encoder to extract five feature maps of different dimensions. The specific calculations are as follows:

[0014]

[0015]

[0016] in, This represents the convolution of three subgroups of the SE(3) group convolution. , For the fixed and moving images in the i-th dimension, , Let i be the fixed image feature map and the moving image feature map of the i-th dimension.

[0017] Furthermore, Step 1.2 includes:

[0018] Given a 3D rotation matrix R, SE(3) and Then the SE(3) group convolution is defined as follows:

[0019]

[0020] in, Represents n-dimensional space, , The signal and kernel are respectively located in the SE(3) space, with position x ∈ Rotation R∈ SO(3), , The integral variable is R, which is the rotation matrix, and SO(3) is the three-dimensional rotation group. The output is... Let f be the convolution response at the group element (x, R), representing the correlation between the signal f and the kernel k under the group action. The convolution kernel... middle The translation of the group, Represents the rotating part. Represents the input signal;

[0021] The input signal is boosted to SE(3); the definition of boosted convolution is as follows:

[0022]

[0023] For the input signal, the convolution kernel for The function above, but its input has been rotated, that is... Output The function defined on SE(3) after rotation is expressed as the correlation between signal f and kernel k at position x with direction R as the reference coordinate system;

[0024] set up and These represent the indices of the input and output channels, respectively; the SE(3) core is separated as follows:

[0025]

[0026] in, Represents a complete SE(3) convolution kernel. This is represented as the rotated part of the SE(3) convolution kernel. It is represented as the spatial part of the SE(3) convolution kernel.

[0027] Furthermore, Step 2 includes:

[0028] Step 2.1, fix the image and moving images The initial deformation field is obtained as input. 1;

[0029] Step 2.2, Deformation Field in the First Stage 1 pair of motion image feature maps in the fourth dimension Perform deformation and output feature map , With the fixed image feature map of the fourth dimension F 4The deformation field of the second stage is then obtained as input. 2; 2 pairs of motion image feature maps in the third dimension M 3 Perform deformation and output feature map , Compared with the fixed image feature map in the third dimension F 3 Then, as input, the deformation field of the third stage is obtained. 3. By analogy, the subsequent deformation field can be derived. 4, 5;

[0030] Step 2.3: After the deformation fields of all stages are generated, the deformation fields of the five stages are superimposed to obtain the final deformation field.

[0031] Further, Step 2.1 includes:

[0032] In the Transformer-subgroup convolutional fusion encoder, the input image is first subjected to linear projection. and normalization layer The input to the Transformer is flattened into a sequence form. After the output of the Transformer is reshaped, it is fed into a triple subgroup convolution module for feature extraction, generating two sets of feature sequences. F 1 - F 5 , M 1 - M 5 ;

[0033] Feature mapping and After linear projection and normalization layer Get query s and keys :

[0034]

[0035]

[0036] Where S represents the sequence length, It is the query vector at the S-th position in the sequence. It is the key vector at the S-th position in the sequence. The linear projection operation uses shared weights, and the weights are initialized from... Start sampling, initialize the bias to 0; any given point The surrounding neighborhood is used The calculation of multi-headed neighborhood attention (NA) is obtained by the following formula:

[0037]

[0038] in, is a learnable bias of the relative position of the neighborhood, initialized to zero; s is the index of the attention head, and n represents the neighborhood size. For normalization, Let this be the query vector at position p in the s-th attention head. This can be represented as the transpose of the set of key vectors at all positions in the neighborhood of p in the s-th attention head. It is the relative position offset of the neighborhood of the s-th attention head;

[0039] Finally, the multiple deformable subfields of this layer are obtained by calculating the neighborhood attention map-weighted regular displacement field:

[0040]

[0041] in, , These are represented as height, width, and length, respectively. Let it be the deformation displacement vector of position p under the s-th attention head. It represents the relative position coordinates of the neighborhood centroids. No learning is required, and multi-head attention relationships can be naturally transformed into multi-coordinate relationships.

[0042] Further, Step 2.2 includes:

[0043] The deformation field obtained in the first stage is upsampled and the fourth dimension of the input motion image feature map is used. Perform a warp transformation, the result after warping With the fixed image feature map of the fourth dimension F 4 It will be sent to the next stage of processing;

[0044]

[0045]

[0046] in, , These are the deformation subfield obtained in the first stage and the final deformation field, respectively. For the upsampling process, For spatial transformation networks based on deformation fields right Perform a distortion transformation.

[0047] Furthermore, Step 2.3 includes:

[0048] By superimposing deformation fields at five different size stages, the triple subgroup convolutional pyramid registration network obtains the final deformation field of the PET / CT image. :

[0049] ;

[0050] Among them, symbols This represents the composition of deformation fields, with the composition order being the coarsest-scale deformation field obtained first. Combining sequentially to the final finest scale .

[0051] Furthermore, in Step 3, the final deformation field obtained in Step 2 is applied to the original-sized moving image using a spatial transformation network, namely the STN network, to perform a differentiable distortion transformation, thereby generating a geometrically corrected image output and realizing the correction of breathing motion artifacts.

[0052] Furthermore, Step 4 includes:

[0053] Define and compute a loss function to quantitatively evaluate the degree of difference between the registered image and the reference image; minimize this loss function through the backpropagation algorithm to drive network parameter optimization, so that the registered image approximates the reference image as closely as possible in spatial structure, thus ensuring registration accuracy;

[0054]

[0055] in, It is a fixed image. It is a moving image with motion artifacts. It is the final deformation field. The similarity loss is based on normalized cross-correlation calculation using a local window. The regularization loss is based on the L2 norm of the final deformation field gradient. It is a regularization parameter. The gradient of the final deformation field.

[0056] The present invention also provides a PET / CT image respiratory motion artifact correction system based on triple subgroup convolutional networks, the system comprising: a module for executing the PET / CT image respiratory motion artifact correction method based on triple subgroup convolutional networks.

[0057] The beneficial effects of this invention are:

[0058] 1. The present invention proposes a lightweight triple subgroup convolution kernel, which focuses on analyzing the rotation and translation features of the coronal, sagittal and transverse planes closely related to PET / CT images, so as to achieve efficient detailed analysis in small clinical sample cases, especially with extremely high resolution for organs and tumors;

[0059] 2. The present invention combines the construction of a Transformer-subgroup convolutional fusion encoder and a pyramid network to construct a triple subgroup convolutional registration network, which can combine multiple dimensions of sub-deformation fields to obtain a smooth deformation field. The deformation field is then used to perform spatial distortion transformation to achieve the purpose of artifact correction.

[0060] 3. The triple subgroup convolution proposed in this invention effectively reduces the model's data requirements and has excellent convergence stability and generalization ability under clinical small sample training conditions. It can capture the morphological changes and local details of the lungs and tumors during respiratory motion with extreme precision, thereby achieving high-precision correction of motion artifacts and improving image quality. Attached Figure Description

[0061] Figure 1 This is a flowchart from the present invention;

[0062] Figure 2 This is a basic structural diagram of the triple subgroup convolutional pyramid registration network used in this invention;

[0063] Figure 3 This is a structural diagram of the Transformer-subgroup convolutional fusion encoder used in this invention;

[0064] Figure 4 These are simulations of the correction results of the method of this invention under different planes of the human lung;

[0065] Figure 5 These are the correction results of the present invention under different aspects of clinical PET data. Detailed Implementation

[0066] Example 1: As Figures 1-5 As shown, a method for correcting respiratory motion artifacts in PET / CT images based on triple subgroup convolutional networks is described, the method comprising:

[0067] Step 1: First, define a new triple subgroup convolution kernel. The triple subgroup convolution kernel specializes in the rotational motion features of the coronal, sagittal, and transverse planes to achieve hierarchical analysis of three-dimensional PET / CT images.

[0068] Step 2: Construct a triple subgroup convolutional pyramid registration network by combining the Transformer-subgroup convolutional fusion encoder to achieve the fusion of multi-dimensional sub-deformation fields into the final deformation field;

[0069] Step 3: Use the STN network to distort the final deformation field to achieve artifact correction.

[0070] Step 4: Calculate the similarity between the registered image and the fixed image using a loss function.

[0071] Further, Step 1 includes:

[0072] Step 1.1: Define Lie groups and group convolution;

[0073] Definition 1: A group is a set G plus a binary operation (usually called group multiplication) that satisfies closure, associativity, identity, and inverse. A Lie group is a mathematical object that simultaneously possesses group structure and smooth manifold structure, where the group operations (multiplication and inversion) are smooth mappings.

[0074] Definition 2: Group Convolution: Group convolution is a generalization of the traditional convolution operation to groups, used to extract features by leveraging the symmetry of groups. Convolution relies on translational symmetry; while group convolution extends this idea to more general groups, such as rotation groups or scaling groups. The formal definition is as follows:

[0075] set up It is a group, a function and This represents the input features and the convolution kernel.

[0076]

[0077] in yes The left-invariant Haar measure ensures that the integral remains invariant under group transformations. For discrete groups, the integral is replaced by a summation.

[0078] Step 1.2: Based on the meaning of Lie groups and group convolution, select SE(3) group as the unit element to construct a triple subgroup convolution kernel. Its rotation axes (x, y, z) correspond to the coronal plane, sagittal plane and transverse plane respectively. Each rotation axis corresponds to four subgroups, and each group of four subgroups is a combination. Each subgroup independently performs isovariant convolution operation under the corresponding rotation transformation.

[0079] Step 1.3: Fix the image and moving images The input images are fed into a Transformer-subgroup convolutional fusion encoder to extract feature maps of five different dimensions. The input images are first processed by linear projection (... ) and normalization layer ( The input is flattened into a sequence form and fed into the Transformer encoder. The Transformer consists of multiple stacked coding layers, each containing a multi-head self-attention mechanism (MSA) and a feedforward network (FFN). After reshaping the Transformer's output, it is fed into a triple subgroup convolutional module for feature extraction, specifically calculated as follows:

[0080]

[0081]

[0082] in, This represents the convolution of three subgroups of the SE(3) group convolution. , For the fixed and moving images in the i-th dimension, , Let i be the fixed image feature map and the moving image feature map of the i-th dimension.

[0083] Furthermore, Step 1.2 includes:

[0084] Given a 3D rotation matrix R, SE(3) and Then the SE(3) group convolution is defined as follows:

[0085]

[0086] in, Represents n-dimensional space, , The signal and kernel are respectively located in the SE(3) space, with position x ∈ Rotation R∈ SO(3), , The integral variable is R, which is the rotation matrix, and SO(3) is the three-dimensional rotation group. The output is... Let f be the convolution response at the group element (x, R), representing the correlation between the signal f and the kernel k under the group action. The convolution kernel... middle The translation of the group, Represents the rotating part. Represents the input signal;

[0087] Since the input data is usually not defined on SE(3), and medical volumetric images are generally in... Therefore, the input signal is boosted to SE(3) as defined above; the definition of boosted convolution is as follows:

[0088]

[0089] For the input signal, the convolution kernel for The function above, but its input has been rotated, that is... Output The function defined on SE(3) after rotation is expressed as the correlation between signal f and kernel k at position x with direction R as the reference coordinate system;

[0090] set up and These represent the indices of the input and output channels, respectively; the SE(3) core is separated as follows:

[0091]

[0092] in, Represents a complete SE(3) convolution kernel. This is represented as the rotated part of the SE(3) convolution kernel. It is represented as the spatial part of the SE(3) convolution kernel.

[0093] Furthermore, Step 2 includes:

[0094] Step 2.1, fix the image and moving images The initial deformation field is obtained as input. 1;

[0095] Step 2.2, Deformation Field in the First Stage 1 pair of motion image feature maps in the fourth dimension Perform deformation and output feature map , With the fixed image feature map of the fourth dimension F 4 The deformation field of the second stage is then obtained as input. 2; 2 pairs of motion image feature maps in the third dimension M 3 Perform deformation and output feature map , Compared with the fixed image feature map in the third dimension F 3 Then, as input, the deformation field of the third stage is obtained. 3. By analogy, the subsequent deformation field can be derived. 4, 5;

[0096] Step 2.3: After the deformation fields of all stages are generated, the deformation fields of the five stages are superimposed to obtain the final deformation field.

[0097] Further, Step 2.1 includes:

[0098] In the Transformer-subgroup convolutional fusion encoder, the input image is first subjected to linear projection. and normalization layer The input to the Transformer is flattened into a sequence form. After the output of the Transformer is reshaped, it is fed into a triple subgroup convolution module for feature extraction, generating two sets of feature sequences. F 1 - F 5 , M 1 - M 5 ;

[0099] Feature mapping and After linear projection and normalization layer Get query s and keys :

[0100]

[0101]

[0102] Where S represents the sequence length, It is the query vector at the S-th position in the sequence. It is the key vector at the S-th position in the sequence. The linear projection operation uses shared weights, and the weights are initialized from... Start sampling, initialize the bias to 0; any given point The surrounding neighborhood is used The calculation of multi-head neighborhood attention (NA) is given by the following formula:

[0103]

[0104] in, is a learnable bias of the relative position of the neighborhood, initialized to zero; s is the index of the attention head, and n represents the neighborhood size. For normalization, Let this be the query vector at position p in the s-th attention head. This can be represented as the transpose of the set of key vectors at all positions in the neighborhood of p in the s-th attention head. It is the relative position offset of the neighborhood of the s-th attention head;

[0105] Finally, the multiple deformable subfields of this layer are obtained by calculating the neighborhood attention map-weighted regular displacement field:

[0106]

[0107] in, , These are represented as height, width, and length, respectively. Let it be the deformation displacement vector of position p under the s-th attention head. It represents the relative position coordinates of the neighborhood centroids. No learning is required, and multi-head attention relationships can be naturally transformed into multi-coordinate relationships.

[0108] Further, Step 2.2 includes:

[0109] The deformation field obtained in the first stage is upsampled and the fourth dimension of the input motion image feature map is used. Perform a warp transformation, the result after warping With the fixed image feature map of the fourth dimension F 4 The image is then sent to the next stage for processing. This multi-scale processing mechanism ensures that the network branches can gradually recover and finely depict image details based on high-level context information, thereby effectively improving the modeling ability of artifacts and local tumor features and the generalization performance of the network.

[0110]

[0111]

[0112] in, , These are the deformation subfield obtained in the first stage and the final deformation field, respectively. For the upsampling process, For spatial transformation networks based on deformation fields right Perform a distortion transformation.

[0113] Furthermore, Step 2.3 includes:

[0114] By superimposing deformation fields at five different size stages, the triple subgroup convolutional pyramid registration network obtains the final deformation field of the PET / CT image. :

[0115] ;

[0116] Among them, symbols This represents the composition of deformation fields, with the composition order being the coarsest-scale deformation field obtained first. Combining sequentially to the final finest scale .

[0117] Furthermore, in Step 3, the final deformation field obtained in Step 2 is applied to the original-sized moving image using a spatial transformation network, namely the STN network, to perform a differentiable distortion transformation, thereby generating a geometrically corrected image output and realizing the correction of breathing motion artifacts.

[0118] Furthermore, Step 4 includes:

[0119] Define and compute a loss function to quantitatively evaluate the degree of difference between the registered image and the reference image; minimize this loss function through the backpropagation algorithm to drive network parameter optimization, so that the registered image approximates the reference image as closely as possible in spatial structure, thus ensuring registration accuracy;

[0120]

[0121] in, It is a fixed image. It is a moving image with motion artifacts. It is the final deformation field. The similarity loss is based on normalized cross-correlation calculation using a local window. The regularization loss is based on the L2 norm of the final deformation field gradient. It is a regularization parameter. The gradient of the final deformation field.

[0122] The present invention also provides a PET / CT image respiratory motion artifact correction system based on triple subgroup convolutional networks, the system comprising: a module for executing the PET / CT image respiratory motion artifact correction method based on triple subgroup convolutional networks.

[0123] In one feasible implementation, it further includes:

[0124] Step 5: Evaluate the model using simulation data and clinical data;

[0125] Step 6: Further optimize the model parameters to obtain the optimal artifact-corrected PET / CT images.

[0126] Specifically, Step 5 includes: Building a simulation environment for PET / CT research based on the GEANT4 Application for Tomographic Emission (GATE) v8.0 Monte Carlo simulation platform. Simultaneously, an NCAT digital human body model based on non-uniform rational B-splines (NURBs) technology is used, with a respiratory cycle set to 5 seconds and a diaphragm movement range between 1 cm and 3 cm. Different substances are differentiated by setting different levels of radioactivity to simulate scanning and generate lung pixel membranes with an image size of 128×128×32. The training and test sets of the simulation dataset are divided using an 8:2 ratio. The medical imaging equipment for clinical data acquisition is a Philips Ingenuity TF PET / CT scanner. Tracers are used. 18 F-FDG was synthesized in an existing chemical synthesis module with a radiochemical purity >95%. The PET / CT scan procedure for each patient was as follows: fasting for at least 6 hours prior to injection, with a blood glucose level below 10 mmol / L, and an injection dose of 0.15 mCi / kg. After 40 minutes of rest following injection, PET scans were performed at two beds centered on the lungs, with each scan lasting 4 minutes. Dynamic images were obtained from 5-minute scans, and stationary images were taken from a single phase within a respiratory-gated sequence. Before being fed into the model, the images were cropped to 96 × 96 × 64 pixels and normalized to zero mean.

[0127] Specifically, in Step 6, the model parameters are further analyzed and optimized based on the test results of simulation data and clinical data to obtain the optimal artifact-corrected PET / CT image.

[0128] Experiment 1: The results of correcting respiratory motion artifacts on the simulated lung membrane using the method of this invention are as follows. Figure 4 The images shown are cross-sectional, coronal, and sagittal images, respectively. The first two columns, from left to right, represent a stationary image without artifacts and a moving image with artifacts, respectively. Analysis of the indicators reveals that the DSC, Ncc, and HD values ​​of the image corrected by VM (VoxelMorph) are 83.99%, 98.03%, and 2.68, respectively. The DSC, Ncc, and HD values ​​of the image corrected by TM (TransMorph) are 88.75%, 98.83%, and 2.43, respectively. The DSC, Ncc, and HD values ​​of the image corrected by ModeT are 88.27%, 98.61%, and 2.46, respectively. The DSC, Ncc, and HD values ​​of the image corrected by the method of this invention are 90.42%, 99.24%, and 2.33, respectively. Analysis of image details shows that only the image corrected by this method is free of artifacts, while other methods all exhibit certain defects. Therefore, the method of this invention can effectively correct respiratory motion artifacts in PET / CT images.

[0129] Experiment 2: Results of clinical data after respiratory motion artifact correction using the method of this invention are as follows. Figure 5 The images shown are cross-sectional, coronal, and sagittal images, respectively. The first two columns, from left to right, represent a fixed image without artifacts and a moving image with artifacts, respectively. Clinical data uses one phase of gated data as a fixed image. As can be seen from the images, due to the influence of respiratory motion, the tumor position in the artifact images is significantly shifted and enlarged, and the tumor boundaries are unclear compared to the fixed images, with overlapping tumors that are indistinguishable. Analysis of the indicators shows that the DSC, Ncc, and HD values ​​of the VM (VoxelMorph) corrected image are 79.89%, 98.50%, and 1.66, respectively. The DSC, Ncc, and HD values ​​of the TM (TransMorph) corrected image are 81.74%, 98.80%, and 1.66, respectively. The DSC, Ncc, and HD values ​​of the ModeT corrected image are 83.73%, 98.39%, and 2.19, respectively. The DSC, Ncc, and HD values ​​of the image corrected by the method of this invention are 87.20%, 99.31%, and 1.32, respectively. Analysis of the corrected image details reveals that only the method of this invention clearly distinguishes the tumor boundaries and corrects the tumor size to the appearance of the fixed image as much as possible; other methods still show some adhesion between tumors. Therefore, the method of this invention can effectively correct respiratory motion artifacts in PET / CT images.

[0130] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for correcting respiratory motion artifacts in PET / CT images based on triple subgroup convolutional networks, characterized in that: The method includes: Step 1: First, define a new triple subgroup convolution kernel. The triple subgroup convolution kernel specializes in the rotational motion features of the coronal, sagittal, and transverse planes to achieve hierarchical analysis of three-dimensional PET / CT images. Step 2: Construct a triple subgroup convolutional pyramid registration network by combining the Transformer-subgroup convolutional fusion encoder to achieve the fusion of multi-dimensional sub-deformation fields into the final deformation field; Step 3: Use the STN network to distort the final deformation field to achieve artifact correction. Step 4: Calculate the similarity between the registered image and the fixed image using a loss function.

2. The method for correcting respiratory motion artifacts in PET / CT images based on triple subgroup convolutional networks according to claim 1, characterized in that: Step 1 includes: Step 1.1: Define Lie groups and group convolution; Step 1.2: Based on the meaning of Lie groups and group convolution, select SE(3) group as the unit element to construct a triple subgroup convolution kernel. Its rotation axes (x, y, z) correspond to the coronal plane, sagittal plane and transverse plane respectively. Each rotation axis corresponds to four subgroups, and each group of four subgroups is a combination. Each subgroup independently performs isovariant convolution operation under the corresponding rotation transformation. Step 1.3: Fix the image and moving images The images are input into a Transformer-subgroup convolutional fusion encoder to extract five feature maps of different dimensions. The specific calculations are as follows: ； ； in, This represents the convolution of three subgroups of the SE(3) group convolution. , For the fixed and moving images in the i-th dimension, , Let i be the fixed image feature map and the moving image feature map of the i-th dimension.

3. The method for correcting respiratory motion artifacts in PET / CT images based on triple subgroup convolutional networks according to claim 2, characterized in that: Step 1.2 includes: Given a 3D rotation matrix R, SE(3) and Then the SE(3) group convolution is defined as follows: ； in, Represents n-dimensional space, , The signal and kernel are respectively located in the SE(3) space, with position x ∈ Rotation R ∈ SO(3), , The integral variable is R, which is the rotation matrix, and SO(3) is the three-dimensional rotation group. The output is... Let f be the convolution response at the group element (x, R), representing the correlation between the signal f and the kernel k under the group action. The convolution kernel... middle The translation of the group, Represents the rotating part. Represents the input signal; The input signal is boosted to SE(3); the definition of boosted convolution is as follows: ； For the input signal, the convolution kernel for The function above, but its input has been rotated, that is... Output The function defined on SE(3) after rotation is expressed as the correlation between signal f and kernel k at position x with direction R as the reference coordinate system; set up and These represent the indices of the input and output channels, respectively; the SE(3) core is separated as follows: ； in, Represents a complete SE(3) convolution kernel. This is represented as the rotated part of the SE(3) convolution kernel. It is represented as the spatial part of the SE(3) convolution kernel.

4. The method for correcting respiratory motion artifacts in PET / CT images based on triple subgroup convolutional networks according to claim 1, characterized in that: Step 2 includes: Step 2.1, fix the image and moving images The initial deformation field is obtained as input. 1; Step 2.2, Deformation Field in the First Stage 1 pair of motion image feature maps in the fourth dimension Perform deformation and output feature map , With the fixed image feature map of the fourth dimension F 4 Then, as input, the deformation field of the second stage is obtained. 2; 2 pairs of motion image feature maps in the third dimension M 3 Perform deformation and output feature map , Compared with the fixed image feature map in the third dimension F 3 Then, as input, the deformation field of the third stage is obtained.

3. By analogy, the subsequent deformation field can be derived. 4, 5; Step 2.3: After the deformation fields of all stages are generated, the deformation fields of the five stages are superimposed to obtain the final deformation field.

5. The method for correcting respiratory motion artifacts in PET / CT images based on triple subgroup convolutional networks according to claim 4, characterized in that: Step 2.1 includes: In the Transformer-subgroup convolutional fusion encoder, the input image is first subjected to linear projection. and normalization layer The input to the Transformer is flattened into a sequence form. After the output of the Transformer is reshaped, it is fed into a triple subgroup convolution module for feature extraction, generating two sets of feature sequences. F 1 - F 5 , M 1 - M 5 ; Feature mapping and After linear projection and normalization layer Get query s and keys : ； ； Where S represents the sequence length, It is the query vector at the S-th position in the sequence. It is the key vector at the S-th position in the sequence. The linear projection operation uses shared weights, and the weights are initialized from... Start sampling, initialize the bias to 0; any given point The surrounding neighborhood is used The calculation of multi-headed neighborhood attention (NA) is obtained by the following formula: ； in, is a learnable bias of the relative position of the neighborhood, initialized to zero; s is the index of the attention head, and n represents the neighborhood size. For normalization, Let this be the query vector at position p in the s-th attention head. This can be represented as the transpose of the set of key vectors at all positions in the neighborhood of p in the s-th attention head. It is the relative position offset of the neighborhood of the s-th attention head; Finally, the multiple deformable subfields of this layer are obtained by calculating the neighborhood attention map-weighted regular displacement field: ； in, , These are represented as height, width, and length, respectively. Let it be the deformation displacement vector of position p under the s-th attention head. It represents the relative position coordinates of the neighborhood centroids. No learning is required, and multi-head attention relationships can be naturally transformed into multi-coordinate relationships.

6. The method for correcting respiratory motion artifacts in PET / CT images based on triple subgroup convolutional networks according to claim 4, characterized in that: Step 2.2 includes: The deformation field obtained in the first stage is upsampled and the fourth dimension of the input motion image feature map is used. Perform a warp transformation, the result after warping With the fixed image feature map of the fourth dimension F 4 It will be sent to the next stage of processing; ； ； in, , These are the deformation subfield obtained in the first stage and the final deformation field, respectively. For the upsampling process, For spatial transformation networks based on deformation fields right Perform a distortion transformation.

7. The method for correcting respiratory motion artifacts in PET / CT images based on triple subgroup convolutional networks according to claim 4, characterized in that: Step 2.3 includes: By superimposing deformation fields at five different size stages, the triple subgroup convolutional pyramid registration network obtains the final deformation field of the PET / CT image. : ； Among them, symbols This represents the composition of deformation fields, with the composition order being the coarsest-scale deformation field obtained first. Combining sequentially to the final finest scale .

8. The method for correcting respiratory motion artifacts in PET / CT images based on triple subgroup convolutional networks according to claim 1, characterized in that: In Step 3, the spatial transformation network, i.e., the STN network, is used to apply the final deformation field obtained in Step 2 to the original size of the moving image, performing a differentiable distortion transformation, thereby generating a geometrically corrected image output to correct breathing motion artifacts.

9. The method for correcting respiratory motion artifacts in PET / CT images based on triple subgroup convolutional networks according to claim 1, characterized in that: Step 4 includes: Define and compute a loss function to quantitatively evaluate the degree of difference between the registered image and the reference image; minimize this loss function through the backpropagation algorithm to drive network parameter optimization, so that the registered image approximates the reference image as closely as possible in spatial structure, thus ensuring registration accuracy; ； in, It is a fixed image. It is a moving image with motion artifacts. It is the final deformation field. The similarity loss is based on normalized cross-correlation calculation using a local window. The regularization loss is based on the L2 norm of the final deformation field gradient. It is a regularization parameter. The gradient of the final deformation field.

10. A PET / CT image respiratory motion artifact correction system based on a triple subgroup convolutional network, characterized in that, The system includes a module for performing the method for correcting respiratory motion artifacts in PET / CT images based on triple subgroup convolutional networks as described in any one of claims 1 to 9.

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