Dual-tracer pet imaging method based on image patch transformer network

Abstract

The application discloses a kind of based on image block Transform network's dual-tracer PET imaging method, the method will mixed tracer concentration map be divided into equal size image block, all image block is flattened and then extracted feature input Transform network, with corresponding single tracer concentration map as true value label, train network to learn the corresponding relationship between the two, separate the concentration map of single tracer from dual-tracer concentration map.The network model used in the application uses attention mechanism completely, does not depend on recurrent neural network or convolutional neural network, can be processed in parallel and expand the receptive field of image in network learning process, pay more attention to time information and spatial information in a larger range, obtain more accurate separation result.Experiments prove that the generalization of the application is less affected by the spatial position misregistration of images in the training data set during the test process compared with other deep learning methods, and has high robustness.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of PET imaging, and particularly relates to a double-tracer PET imaging method based on an image block Transformer network. BACKGROUND

[0002] Positron Emission Tomography (PET) is a medical imaging technology that records the concentration distribution of a tracer in the body by injecting a radioactive tracer into the body, and can image the physiological information and metabolic state of the organism. PET imaging can monitor pathological changes in the body earlier, and has become a clinical diagnostic tool for tumors and cardiovascular and cerebrovascular diseases. Dynamic double-tracer PET can image the concentration distribution of two tracers in the body in one scan, saving costs while providing more comprehensive complementary information and improving the accuracy of disease diagnosis, so double-tracer PET imaging is a potential clinical diagnostic tool. However, double-tracer PET imaging is challenging. PET images the concentration distribution of a tracer in the body by recording each pair of gamma photons with the same energy and opposite directions. Since the gamma photons emitted by different tracers have the same energy (511 keV), it is difficult to distinguish the signals emitted by different tracers in double-tracer PET imaging. Currently, double-tracer PET imaging methods are mainly divided into traditional methods and deep learning methods. Traditional methods are sensitive to tracer pairs, injection intervals and injection sequences, and also require additional blood input functions and other supplementary information. Deep learning methods are not limited by these factors, and the end-to-end feature learning capability can achieve good separation results.

[0003] Deep learning methods have achieved good results in dual-tracer PET imaging. Currently, deep learning methods mainly use recurrent neural network structures and convolutional neural network structures. Recurrent neural networks are generally used to extract the time activity curve of each pixel point from the concentration map for separation. For example, the bidirectional gated recurrent unit with masking [Tong J, Wang C, Liu H. Temporal Information-Guided Dynamic Dual-Tracer PET Signal Separation Network [J]. Medical Physics, 2022, 49(7): 4585-4598] only focuses on the time information and does not consider the connection between each pixel point in the image. Convolutional neural networks input the sinogram or concentration image into the network for processing through convolution. For example, FBP-CNN [Xu J, Liu H. Three-Dimensional Convolutional Neural Networks for Simultaneous Dual-Tracer PET Imaging [J]. Physics in Medicine and Biology, 2019, 64(18): 185016] learns reconstruction and separation in two modules to obtain single-tracer concentration maps from mixed tracer sinograms. This method has high training cost, so a convolutional neural network with a spatiotemporal attention mechanism is proposed. In practical applications, deep learning methods only need to input mixed tracer data to calculate the concentration maps of two single tracers using the network. However, in the process of training the network, the data required includes dual-tracer concentration maps and corresponding single-tracer concentration maps, which need to be registered. In actual scanning, it is difficult to ensure that the physiological state and scanning position of the biological body are consistent in three scans, so there may be spatial position misregistration between the input dual-tracer concentration map and the label in the training data. SUMMARY

[0004] In view of the above, the present application provides a dual-tracer PET imaging method based on an image block Transformer network, which can more widely focus on spatiotemporal information and reduce the influence of position misregistration in the training data on the network model, and recover more accurate single-tracer concentration maps from dual-tracer concentration maps.

[0005] A dual-tracer PET imaging method based on an image block Transformer network, comprising the following steps:

[0006] (1) Dynamic PET scanning of a biological tissue injected with tracer I to obtain a dynamic PET sinogram Y of tracer I I, a dynamic PET sinogram Y of tracer II is obtained by scanning after tracer II is injected after a period of time, i.e. after tracer I is metabolized and excreted in vivo II , Y I and Y II are reconstructed to obtain corresponding single-tracer concentration maps X I and X II , respectively

[0007] (2) After a dynamic PET scan of biological tissue in which tracer I and tracer II are injected simultaneously, a dynamic PET sinogram Y of mixed tracers is obtained dual , Y dual is reconstructed to obtain a concentration map X of mixed tracers dual ;

[0008] (3) Steps (1) to (2) are repeated multiple times to obtain a large number of samples, each group of samples including single-tracer concentration maps X I and X II and a concentration map X of mixed tracers dual , and all samples are divided into a training set, a validation set and a test set in proportion

[0009] (4) A Transformer network model based on image patch is constructed, X dual in the training set samples is taken as the input of the model, and X I and X II are taken as labels, so as to train the network model

[0010] (5) X dual in the test set samples is input into the trained network model, and the corresponding two groups of single-tracer concentration maps can be separated and recovered.

[0011] Further, the Transformer network model is composed of a preprocessing module, an encoding module and a decoding module connected in sequence.

[0012] Further, the specific implementation of the preprocessing module is as follows: firstly, X dualBefore inputting the model, a copy is stacked together, so that the image data dimension of the input model is bxcxhwx, b is the batch number, c is twice the number of time frames set by dynamic PET scanning, h and w are the length and width of the PET image respectively; After the image data is input into the model, it is divided into n image blocks of the same size, the size of the image block is pxp, and each image block is flattened into a one-dimensional vector with the time dimension. Then, feature extraction is performed through a linear layer, and a feature vector matrix of dimension nxd is obtained for each batch, where d is the dimension of the feature vector. Then, an extra learned vector is concatenated at the front of the feature vector matrix, the initial value of the vector is random and follows a standard normal distribution. Finally, the feature vector matrix of dimension (n+1)x d X is batch input into the encoding module and the decoding module.

[0013] Further, the encoding module is composed of 6 encoding blocks in cascade, each encoding block is composed of Multi-Head Attention, Add&Norm, Feed Forward, Add&Norm four-layer structure connected in turn; The decoding module is composed of 6 decoding blocks in cascade, each decoding block is composed of Multi-Head Attention, Add&Norm, Multi-Head Attention, Add&Norm, Feed Forward, Add&Norm six-layer structure connected in turn.

[0014] Further, the Multi-Head Attention is composed of 16 Self-Attention, each Self-Attention multiplies the input of Multi-Head Attention with linear transformation matrix W Q , W K and W V respectively to obtain the query vector matrix Q, the key vector matrix K, and the value vector matrix V, then the output result of Self-Attention is calculated by the following formula, and finally the output result of 16 Self-Attention is spliced and passed through a linear layer to obtain the output of Multi-Head Attention;

[0015]

[0016] Where: Attention(Q,K,V) is the output result of Self-Attention, s is the column number of the query vector matrix Q, T represents transposition.

[0017] Further, the Feed Forward consists of two linear layers connected, the former linear layer with GELU activation function; the Add&Norm connects the input and output residuals of the former layer and then processes it through layer normalization.

[0018] Further, the input of the Multi-Head Attention in the first encoding block of the encoding module is the feature vector matrix X; the input of the first layer Multi-Head Attention in the first decoding block of the decoding module is the feature vector matrix X with position encoding information added; the query vector matrix Q and the key vector matrix K in the third layer Multi-Head Attention of each decoding block are the results of multiplying the encoding information matrix output by the encoding module and the linear transformation matrix W Q and W K respectively.

[0019] Further, the specific process of training the network model in step (4) is as follows:

[0020] 4.1 Initialize model parameters, including the bias vector and weight matrix of each layer, learning rate, batch number, maximum iteration number and optimizer;

[0021] 4.2 Input X dual in the training set sample to the model, and the model outputs two sets of single tracer corresponding concentration map prediction results through forward propagation, and calculates the loss function L between the prediction results and the labels;

[0022] 4.3 According to the loss function L, the model parameters are continuously updated by the optimizer through gradient descent method until the loss function L converges or the maximum iteration number is reached, and the training is completed;

[0023] 4.4 During the training process, the model is verified and the parameters are fine-tuned by using the validation set sample.

[0024] Further, the function expression of the loss function L is as follows:

[0025]

[0026] Wherein: and are the concentration map prediction results corresponding to the two sets of single tracers output by the model, MSE() represents the mean square error, SSIM() represents the structural similarity, and a and β are weight factors.

[0027] The mixed tracer concentration map is divided into image blocks of equal size, all of which are flattened and then input into a Transformer network for feature extraction, with the corresponding single tracer concentration map as the true value label, and the network is trained to learn the corresponding relationship between the two, so as to separate the single tracer concentration map from the double tracer concentration map. The network model used in the application completely uses an attention mechanism and does not rely on a recurrent neural network or a convolutional neural network, can process in parallel and expand the receptive field of the image in the network learning process, pay more attention to time information and spatial information in a larger range, and obtain more accurate separation results. Different templates, tracer pairs, sampling times and noises are used in the experiment, which proves the generalization of the application. Compared with other deep learning methods, the application is less affected by the spatial position misregistration of the image in the training data set during the test process, and has high robustness. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1 It is a flow architecture schematic diagram of the Transformer network model of the application.

[0029] Figure 2 It is a coding and decoding structure schematic diagram of the Transformer network of the application.

[0030] Figure 3 It is a two-dimensional brain template and a three-dimensional Zubal template used in the embodiment of the application, from left to right are the 15th, 25th and 35th slices of the two-dimensional brain template and the three-dimensional Zubal template.

[0031] Figure 4 It is the separation result of tracer 18 F-FDG, the sampling time is 40min, from left to right are the true value image, the prediction concentration map of the application, U-net and MB-BGRU, from top to bottom are the concentration maps of the 5th, 10th and 15th frames.

[0032] Figure 5 It is the separation result of tracer 11 C-MET, the sampling time is 40min, from left to right are the true value image, the prediction concentration map of the application, U-net and MB-BGRU, from top to bottom are the concentration maps of the 5th, 10th and 15th frames.

[0033] Figure 6 It is the separation result of tracer 18 F-FDG, from left to right are the true value image, the prediction concentration map of the application, U-net and MB-BGRU, from top to bottom are the concentration maps of the 15th, 20th, 25th and 30th slices.

[0034] Figure 7 as a tracer in three-dimensional template experiments 11 The separation results of C-FMZ are shown in columns from left to right: the ground truth image, the predicted concentration maps of the present invention, U-net, and MB-BGRU methods. The rows from top to bottom are the concentration maps of slices 15, 20, 25, and 30.

[0035] Figure 8 Box plots are provided for the evaluation metrics of the two sets of experiments. (a), (c), and (e) show the MSE, MS-SSIM, and PSNR metrics of the two-dimensional template experiment, while (b), (d), and (f) show the MSE, MS-SSIM, and PSNR metrics of the three-dimensional template experiment. The first three figures in each plot are the results of the present invention, U-net, and MB-BGRU in tracer I, and the last three figures are the results in tracer II. Detailed Implementation

[0036] To describe the present invention in more detail, the technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0037] This invention relates to a dual-tracer PET imaging method based on an image-blocking Transformer network, comprising the following steps:

[0038] (1) Prepare data.

[0039] 1.1 Dynamic PET scanning was performed on biological tissue injected with tracer I to obtain the dynamic PET sine curve Y of tracer I. I After a period of time, once the first tracer has been metabolized and excreted from the body, tracer II is injected, and the dynamic PET sine curve Y of tracer II is obtained. II , for Y I and Y II Reconstruction yields the corresponding single-tracer concentration map X. I and X II .

[0040] 1.2 Simultaneous injection of tracer I and tracer II into biological tissues, followed by dynamic PET scanning, yields a dual-tracer dynamic PET sine curve Y. dual In the simulation experiment, Y I and Y II Adding them together gives Y dual , for Y dual Reconstruction yielded the concentration map X of the mixed tracer. dual .

[0041] 1.3 Repeat steps 1.1 and 1.2 multiple times to obtain a large amount of data. Each pair of data includes a single tracer concentration plot X. I and X II, and the corresponding mixed tracer concentration map X dual The data is proportionally divided into training set, validation set and test set. In the simulation experiment, the double tracer concentration map and the corresponding single tracer concentration map are completely registered. In order to simulate the actual situation, the double tracer concentration map in the training set of the simulation experiment is randomly rotated by a small angle, and is randomly offset by a small distance in the horizontal direction and the vertical direction. The validation set and the test set are not modified.

[0042] (2) Build a Transformer network model based on image blocking, the process architecture is as shown in Figure 1 The double tracer concentration map is copied and stacked before inputting into the network model. The data dimension of input network is b x c x h x w, b is the batch number, c is twice the time frame number of dynamic PET scan setting, h and w are the length and width of the image. After the image is input into the network, it is divided into n image blocks of the same size, the size of the image block is p x p, and each image block is flattened into a one-dimensional vector with the time dimension. Then, the feature is extracted through the linear layer, and each batch obtains a vector matrix with a dimension of R n×d , where n is the number of image blocks, d is the dimension of the feature vector, and an additional learning vector is spliced at the front of the obtained vector matrix. The vector matrix is input into the Transformer encoding and decoding structure. The output matrix of the Transformer encoding and decoding structure has the same dimension as the input matrix. After removing the additional vector at the front, the image dimension of the initial input network is restored through the linear layer processing, and the network finally outputs the two stacked tracer concentration maps.

[0043] The Transformer encoding and decoding structure is as shown in Figure 2 There are 6 encoding blocks and 6 decoding blocks. The input of the first encoding block in the encoding structure is the initial vector matrix, and the input of the subsequent encoding blocks is the output of the previous encoding block. After passing through 6 encoding blocks, the encoding structure outputs the encoding information matrix. The input of the first decoding block in the decoding structure is the vector matrix with position encoding information, and the input of the subsequent decoding blocks is the output of the previous decoding block. After passing through 6 decoding blocks, the decoding structure outputs the final result.

[0044] The encoding block has four parts: Multi-Head Attention, Add&Norm, Feed Forward and Add&Norm. Multi-Head Attention is composed of 16 Self-Attention. The input of each Self-Attention is a vector matrix with a dimension of R m×d , m is n plus 1, the vector matrix and the linear transformation matrices W Q , W K and W VQ, K and V are multiplied to get the output calculated by the following formula:

[0045]

[0046] where s is the number of columns of matrix Q, K and V, and softmax is calculated for each row of the matrix:

[0047]

[0048] The output of each Self-Attention is a matrix of dimension R m×s , and the 16 output matrices are concatenated and passed through a linear layer to get a matrix of dimension R m×d , which is the output of Multi-Head Attention.

[0049] Feed Forward consists of two linear layers, the first with a GELU activation function and the second without, represented by the formula:

[0050] Feed Forward(x) = W2GELU(W1x + b1) + b2

[0051] Add&Norm includes residual connection and layer normalization, represented by the formula:

[0052] Add&Norm(x) = LayerNorm(x + F(x))

[0053] where LayerNorm represents layer normalization, which normalizes different channels of the same sample, and F(x) represents the matrix x calculated by Multi-Head Attention or Feed Forward.

[0054] The decoding block has 6 parts: Multi-Head Attention, Add&Norm, Multi-Head Attention, Add&Norm, Feed Forward and Add&Norm, most of which are the same as the encoding block. The second Multi-Head Attention is different from the previous one, and the difference is that the Q and K matrices are the product of the encoding information matrix output by the encoding structure and W Q and W K .

[0055] The vector matrix input into the first decoding block adds position encoding information, and the formula used is as follows:

[0056]

[0057]

[0058] where pos is the position of the image block, d is the dimension of the vector, 2i and 2i+1 represent even and odd dimensions, both of which are less than or equal to d, this encoding can adapt to more vectors, and the relative position is considered.

[0059] (3) X dual in the training set is input into the network, X I and X II are the labels of the network, and the network model is trained to recover the single tracer concentration map from the double tracer concentration map, and the training process is as follows:

[0060] 3.1 Set the optimizer, learning rate, batch number and maximum iteration number, and initialize the network parameters.

[0061] 3.2 The mixed tracer concentration map X dual in the training set is randomly batched and input into the network, and the corresponding single tracer concentration map X I and X II are the true value labels of the network, and the network outputs the predicted concentration maps of the two tracers and The loss function L between the predicted concentration map and the true value label is calculated:

[0062]

[0063] where: a and β are weight factors for balancing MSE and SSIM, set to 1 and 0.02 during training. MSE calculates the mean square error between the predicted image and the true value label, and evaluates the difference between each pixel value in the predicted image and the true value image, and the calculation formula is as follows:

[0064]

[0065] where: and X represent the predicted concentration map and the true value image, and x i represent the values of the predicted concentration map and the true value image at the i-th pixel point, and N represents the number of pixels.

[0066] SSIM calculates the structural similarity between the predicted image and the true value label, and measures the similarity of the image in brightness, contrast and structure, and the calculation formula is:

[0067]

[0068] where: μ x and σ x represent the mean and standard deviation of X, and represent the mean and standard deviation of the covariance of X and c1 and c2 are constants used to prevent the denominator from being zero, which is related to the range of pixel values in the ground truth image.

[0069] 3.3 Update the network parameters using gradient descent, and use the validation set to verify the network model during the training process. When the loss function converges to the minimum or the number of training iterations reaches the maximum iteration number, the training is completed.

[0070] (4) Obtain the double-tracer concentration map X dual Input the trained network model to obtain the corresponding two single-tracer concentration maps.

[0071] In the following, we verify the effectiveness of the present application based on simulation experiments. The two-dimensional brain template and the three-dimensional Zubal template are selected for the experiments. The size of the two-dimensional brain template is 160*200, and there are 9 regions of interest (ROIs). The size of the three-dimensional Zubal template is 128*128, and there are a total of 40 slices. The template has 5 ROIs, and different slices contain different ROIs. The first 21 slices contain two ROIs, the 22nd to 27th slices contain three ROIs, and the last 13 slices contain five ROIs. Figure 3 From left to right are the two-dimensional brain template, the 15th, 25th, and 35th slices of the three-dimensional Zubal template. The tracer pair used for the two-dimensional brain template is 18 F-FDG+ 11 C-MET, and the tracer pair used for the three-dimensional Zubal template is 18 F-FDG+ 11 C-FMZ. The kinetic characteristics of different tracers are simulated using a kinetic parameter-based compartment model. The specific sampling protocol settings are shown in Table 1:

[0072] Table 1

[0073]

[0074] The simulated PET scanner is the Inveon micro-PET of Siemens. The PET detector ring of this model is composed of 16 detector blocks, each detector block is composed of 4 detectors, and each detector is composed of 20*20 arranged lutetium oxyorthosilicate crystals. The diameter of the ring is 161 mm, the cross-sectional field of view is 100 mm, and the axial field of view is 127 mm. The sinogram of the single tracer is obtained using the COMKAT and Fessler toolboxes of MATLAB, and the corresponding concentration map is reconstructed using the OSEM reconstruction algorithm.

[0075] Two-dimensional template generates 600 groups of dynamic PET data, each group of data contains 18 time frames, of which 480 groups are used for training, 60 groups are used for verification, and 60 groups are used for testing, the training set, the verification set and the test set have different kinetic parameters, the double tracer concentration map in the training set is rotated by randomly selecting angle number between-3° and 3°, and the pixel number is randomly selected between-3 and 3, and the horizontal and vertical directions are respectively translated by different distances. Three-dimensional template generates 30x40 groups of dynamic PET data, each group of data contains 18 time frames, of which 960 groups are used for training, 120 groups are used for verification, and 120 groups are used for testing, the training set, the verification set and the test set have different kinetic parameters, the double tracer concentration map in the training set is rotated by randomly selecting angle number between-5° and 5°, and the pixel number is randomly selected between-5 and 5.

[0076] The mixed tracer concentration map X in the training set is rotated by randomly selecting angle number between-3° and 3°, and the pixel number is randomly selected between-3 and 3, and the horizontal and vertical directions are respectively translated by different distances. dual Batch input network, corresponding two single tracer concentration maps X I and X II As the true value label, the network is trained, the network selects Adam optimizer, the learning rate is set to 0.0002 during training, the batch number is set to 1, and the maximum iteration number is set to 100. After that, the mixed tracer concentration map X in the test set is rotated by randomly selecting angle number between-3° and 3°, and the pixel number is randomly selected between-3 and 3, and the horizontal and vertical directions are respectively translated by different distances. dual Input the trained model, output the corresponding two tracer single injection prediction concentration maps and

[0077] Figure 4 and Figure 5 is the experimental result of two-dimensional template at a sampling time of 40 min, Figure 4 is the separation result of tracer 18 F-FDG, Figure 5 is 11 the separation result of C-MET, the two pictures show the concentration maps of the 5th, 10th and 15th frames from top to bottom, and it can be seen that the concentration change trend of the tracer, 18 the concentration of F-FDG increases with time, 11C-MET has a high initial concentration and then a downward trend. The comparison method selects a convolutional neural network with a spatio-temporal attention mechanism (the network is based on U-net, hereinafter referred to as U-net) and a mask-based bidirectional gated recurrent unit (MB-BGRU), both of which use a convolutional neural network structure and a recurrent neural network structure. From left to right in the figure are the true value image, the predicted concentration image of the application, U-net and MB-BGRU, it can be seen that the MB-BGRU method that only focuses on time information has obvious noise separation and is relatively fuzzy, and the results of the other two methods have clear boundaries and good detail recovery, among which the application and the true value image are closer.

[0078] Figure 6 and Figure 7 is the separation result of the three-dimensional template, Figure 6 is the tracer 18 is the separation result of F-FDG, Figure 7 is 11 is the separation result of C-FMZ, the 10th frame is selected, and from left to right in the figure are the true value image, the predicted results of the application, U-net and MB-BGRU, and from top to bottom are the concentration images of the 15th, 20th, 25th and 30th slices. It can be seen from the figure that the result image of the MB-BGRU method is fuzzy; the U-net method has a simple image structure at the 15th and 20th slices, and the result is similar to the label, but at the 25th and 30th slices, the image structure becomes complex, and the structure below the predicted concentration image is different from the true value; the result image of the application is clear and closest to the true value.

[0079] Figure 8 is the box plot of the evaluation index of the two groups of experiments, wherein (a), (c) and (e) are the MSE index, MS-SSIM index and PSNR index of the two-dimensional template experiment, (b), (d) and (f) are the MSE index, MS-SSIM index and PSNR index of the three-dimensional template experiment, and from left to right in each figure are the indexes of the application, U-net and MB-BGRU on the two tracers, it can be seen that the average of the evaluation indexes of the application is higher than those of the other two methods, and the separation result is stable and has small fluctuations, which shows the superiority of the application.

[0080] The experimental results show that the double-tracer PET imaging method based on the image block Transformer network is effective, can reduce the error caused by spatial position misregistration in the training data set, and realizes more accurate and reliable separation. Different template shapes also show that the generalization and robustness of the application are high.

[0081] The above description of the embodiments is to assist those of ordinary skill in the art to understand and apply the present application. Those skilled in the art can easily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative labor. Therefore, the present application is not limited to the above embodiments, and improvements and modifications made to the present application by those skilled in the art based on the disclosure of the present application should be within the scope of protection of the present application.

Claims

1. A double-tracer PET imaging method based on image patch-based Transformer network, comprising the following steps: (1) Dynamic PET scanning was performed on the biological tissue injected with tracer I to obtain the dynamic PET sine curve Y of tracer I. I After a period of time, once tracer I has been metabolized and excreted from the body, tracer II is injected, and the dynamic PET sine wave Y of tracer II is obtained by scanning. II For Y respectively I and Y II Reconstruction yields the corresponding single-tracer concentration map X. I and X II ; (2) after dynamic PET scanning of the biological tissue injected with tracer I and tracer II at the same time, a dynamic PET sinogram Y of the mixed tracer is obtained dual , Y is reconstructed to obtain a concentration map X of the mixed tracer dual dual ;​ (3) repeat steps (1)-(2) multiple times to obtain a large number of samples, each group of samples including a single tracer concentration map X I and X II and a concentration map X of the mixed tracer dual , and divide all samples into training set, validation set and test set in proportion; (4) constructing a Transformer network model based on image patches, taking X dual as the model input, X I and X II as the label, so as to train the network model; The Transformer network model is composed of a preprocessing module, an encoding module, and a decoding module connected in sequence, and the loss function L of the model is expressed as follows: wherein: and The model outputs two sets of concentration map prediction results corresponding to the single tracer, MSE() represents the mean square error, SSIM() represents the structural similarity, and a and β are weight factors. (5) X from the test set samples dual By inputting the data into the trained network model, the corresponding two sets of single tracer concentration maps can be separated and recovered.

2. The dual-tracer PET imaging method of claim 1, wherein: The specific implementation of the preprocessing module is: first, X dual Before inputting the model, a copy is stacked together, so that the image data dimension of the input model is bxcxhwx, b is the batch number, c is twice the number of time frames set by dynamic PET scanning, h and w are the length and width of the PET image respectively; After the image data is input into the model, it is divided into n image blocks of the same size, the size of the image block is pxp, each image block is flattened into a one-dimensional vector with the time dimension, then feature extraction is performed through the linear layer, each batch obtains a feature vector matrix with a dimension of nx d, where d is the dimension of the feature vector, and then an extra learning vector is spliced in the front of the feature vector matrix, the initial value of the vector is random and subject to standard normal distribution, finally the feature vector matrix with a dimension of (n+1)xd is input into the encoding module and the decoding module.

3. The dual-tracer PET imaging method of claim 2, wherein: The encoding module is composed of 6 encoding blocks connected in cascade, and each encoding block is composed of Multi-Head Attention, Add&Norm, Feed Forward, and Add&Norm four-layer structures connected in sequence; the decoding module is composed of 6 decoding blocks connected in cascade, and each decoding block is composed of Multi-Head Attention, Add&Norm, Multi-Head Attention, Add&Norm, Feed Forward, and Add&Norm six-layer structures connected in sequence.

4. The dual-tracer PET imaging method of claim 3, wherein: The Multi-Head Attention is composed of 16 Self-Attention, each of which respectively multiplies the input of the Multi-Head Attention by linear transformation matrices W Q , W K , and W V to obtain a query vector matrix Q, a key vector matrix K, and a value vector matrix V, and then calculates the output result of the Self-Attention by the following formula, and finally splices the output results of the 16 Self-Attention and passes through a linear layer to obtain the output of the Multi-Head Attention. Wherein: Attention(Q, K, V) is the output result of Self-Attention, s is the column number of the query vector matrix Q, and T represents transposition.

5. The dual-tracer PET imaging method of claim 3, wherein: The Feed Forward is composed of two linear layers connected in sequence, and the first linear layer has a GELU activation function; the Add&Norm connects the input and output residual of the previous layer and then performs layer normalization processing.

6. The dual-tracer PET imaging method of claim 3, wherein: The input of the Multi-Head Attention of the first encoding block in the encoding module is the feature vector matrix X; the input of the first layer Multi-Head Attention of the first decoding block in the decoding module is the feature vector matrix X added with the position encoding information; the query vector matrix Q and the key vector matrix K of the Multi-Head Attention of the third layer in each decoding block are the results obtained by multiplying the encoding information matrix output by the encoding module and the linear transformation matrices W Q and W K respectively.

7. The dual-tracer PET imaging method of claim 1, wherein: The specific process of training the network model in step (4) is as follows: 4.1 Initialize the model parameters, including the bias vector and weight matrix of each layer, learning rate, batch number, maximum iteration number, and optimizer; 4.2 X from the training set samples dual The input is fed into the model, and the model outputs two sets of concentration map prediction results corresponding to single tracers through forward propagation. The loss function L between the prediction results and the label is calculated. 4.3 According to the loss function L, the model parameters are continuously updated by the gradient descent method using the optimizer until the loss function L converges or the maximum iteration number is reached, and the training is completed; 4.4 During the training process, the model is verified and the parameters are fine-tuned using the validation set samples.

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