CN115423892A - Attenuation-free correction PET reconstruction method based on maximum expectation network - Google Patents

Abstract

The invention discloses a non-attenuation correction PET reconstruction method based on maximum expectation network, which realizes the process of directly reconstructing PET images based on non-attenuation correction measurement data. The method builds a network framework based on EM reconstruction and CNN, and EM is used for reconstruction For rough PET images, CNN is used to improve the quality of PET images. CNN can learn the attenuation mechanism between non-attenuation-corrected measurement data and PET images, and realize attenuation compensation for PET images. The present invention can realize the mapping from sinogram _NAC to PET image without additional CT or MR scanning and attenuation correction for measurement data. In addition, the present invention has fast convergence in the training phase, can quickly obtain the training model, and can quickly obtain the PET image based on the measurement data after the model training is completed.

Description

A Non-Attenuation-Corrected PET Reconstruction Method Based on Maximum Expectation Network

technical field

The invention belongs to the technical field of biomedical image reconstruction, in particular to a PET reconstruction method based on maximum expectation network without attenuation correction.

Background technique

As a medical imaging tool for cancer diagnosis, brain functional imaging, and treatment recovery monitoring, PET (Positron Emission Computed Tomography) enables noninvasive molecular-level information capture of specific targets. Radiotracers usually enter the organism through intravenous injection, nasal inhalation, etc., and participate in the physiological and metabolic reactions of the organism for a period of time. The detector records the spatiotemporal information of the photons to reconstruct the spatial distribution of the tracer.

In recent years, the rapid development of PET reconstructed image quantitative technology has made it widely used in the fields of tissue and organ pathological diagnosis, quantitative analysis of protein biomolecules, drug development and other fields. The dependence of quantitative PET images in various fields has in turn promoted the improvement of PET quantitative accuracy. sex research. Literature [Jin M, Yang Y, Niu X, Marin T, Brankov JG, Feng B, Pretorius PH, King MA, Wernick MN. A quantitative evaluation study of four-dimensional gated cardiac SPECT reconstruction. Phys Med Biol. 2009 Sep 21; 54 (18):5643-59] to obtain quantitative results by introducing and estimating a quantitative coefficient in the PET forward model measurement data. The literature [Joel S.Karp, Suleman Surti, Margaret E.Daube-Witherspoon, Gerd Muehllehner Journal of Nuclear Medicine Mar 2008,49(3)462-470] tries to use time-of-flight (TOF) information to improve the signal-to-noise ratio of the reconstructed image, It is also proved that the introduction of TOF in the reconstruction process can effectively improve the quantification ability. Literature [Kadrmas DJ, Casey ME, Conti M, Jakoby BW, Lois C, Townsend DW. Impact oftime-of-flight on PET tumor detection. J Nucl Med.2009Aug; 50 (8): 1315-23] using TOF The detection improves the accuracy of the photon localization of the line of response (LOR) to improve the quality of the PET reconstruction image; there are also some studies focusing on the introduction of the point spread function (PSF) in the forward modeling of PET imaging, because the PSF can reflect the relationship between photons and organisms. Therefore, the correction of physical effects such as attenuation and scattering can be realized, and the quantitative accuracy of image reconstruction can be improved. However, the reconstruction quality of PET images is still limited by many factors such as the physical effects of imaging, tracking dynamics, and the motion of the measured object or equipment. Among them, photon attenuation, as an unavoidable physical effect in obtaining PET measurement data, seriously affects the quality of PET images. accuracy.

Attenuation correction based on CT or MRI anatomical information in PET/CT or PET/MR imaging systems is currently the commonly used correction method, but in some cases, the information provided by CT or MRI is inaccurate or cannot be obtained at all. Such as regions affected by respiration and cardiac motion in PET/CT and PET/MR, regions affected by metal implants in PET/CT and PET/MR and all regions where reliable MR-based attenuation correction is challenging (e.g. lung), respiration and cardiac motion often create a mismatch between CT-derived attenuation and tracer activity distribution. In PET/MR, often many MR sequences are applied, so most PET data are not acquired simultaneously with MR images for attenuation correction; in PET/CT, attenuation and motion images are never acquired simultaneously. Therefore, any patient movement after CT or MR acquisition will destroy the attenuation image; if the source of attenuation-corrected data is inaccurate, quantitative analysis of PET cannot be performed, so a quantitative PET reconstruction method without attenuation correction is urgently needed.

Contents of the invention

In view of the above, the present invention provides a PET reconstruction method based on maximum expectation network without attenuation correction, which combines maximum expectation algorithm and convolutional neural network (CNN) to realize PET image reconstruction and attenuation compensation.

A PET reconstruction method without attenuation correction based on the maximum expectation network, comprising the following steps:

(1) Utilize the PET system to scan the biological tissue injected with the radioactive tracer to collect and obtain the measurement data sinogram _NAC ;

(2) Perform CT or MR acquisition on the biological tissue injected with radioactive tracer, and then convert the value in the CT or MR image into the attenuation coefficient at 511KeV energy, so as to generate the attenuation map;

(3) correcting the measurement data sinogram _NAC by using the attenuation map to obtain the corrected measurement data sinogram _AC ;

(4) performing PET reconstruction based on the measurement data sinogram _AC , and obtaining the corresponding PET image x _AC ;

(5) Perform multiple scans and reconstructions according to steps (1) to (4) to obtain a large number of samples, each group of samples contains corresponding sinogram _NAC and x _AC , and then divide all samples into training set and test set;

(6) Build a PET reconstruction model based on the maximum expectation network, which includes an initialization module, an EM reconstruction module, and a CNN attenuation compensation module, wherein the initialization module uses the initialization matrix to convert the measurement data sinogram _NAC into an initialization image x ⁽⁰⁾ , and the EM reconstruction module Used to reconstruct the initialization image x ⁽⁰⁾ into a PET image r ⁽¹⁾ , the CNN attenuation compensation module is used to perform attenuation compensation on the PET image r ⁽¹⁾ to obtain the PET image x ⁽¹⁾ output by the first layer iteration, and The EM reconstruction module and the CNN attenuation compensation module are combined as an optimized structure EMCNN and repeated multi-layer iterations, x ⁽¹⁾ is used as the input of the second layer EMCNN, and after multi-layer iterations, the PET image reconstructed by the model is finally output;

(7) Use the sinogram _NAC in the training set sample as the model input, and x _AC as the label to train the PET reconstruction model;

(8) Input the sinogram _NAC in the test set sample into the trained PET reconstruction model, and the corresponding PET image can be directly reconstructed without attenuation correction.

Further, the scanning mode of the PET system in the step (1) can be static scanning or dynamic scanning.

Further, in the step (2), converting the value in the CT or MR image into the attenuation coefficient at 511KeV energy can be realized by scaling, segmenting or mixing segments.

Further, the correction of the measurement data sinogram _NAC in the step (3) includes random correction, normalization correction, dead time correction, scattering correction and attenuation correction.

Further, the initialization matrix expression adopted by the initialization module is as follows:

Q _init ＝xy ^T (yy ^T +λI) ^-1

Among them: Q _init is the initialization matrix, x and y are the x _AC and sinogram _NAC in the training set samples respectively, λ is the regularization coefficient, I is the identity matrix, and ^T is the transpose.

Further, the CNN attenuation compensation module consists of a convolutional layer D1, a batch normalization layer B1, a ReLU activation layer R1, a convolutional layer D2, a soft threshold calculation layer, a convolutional layer D3, and a ReLU activation layer R2 from input to output. , batch normalization layer B2, and convolutional layer D4 are connected sequentially, and the convolution kernels in the four convolutional layers D1-D4 are all 3×3 in size, and the depths are 32, 32, 32, and 1 in sequence.

Further, the process of training the PET reconstruction model in the step (7) is as follows:

6.1 Initialize the model parameters, including the bias vector and weight matrix of each layer, learning rate, optimization method and maximum number of iterations;

6.2 Input the measurement data sinogram _NAC in the training set sample to the model, and the model forward propagates and outputs the reconstructed PET image, and calculates the loss function L between the PET image and the label x _AC ;

6.3 According to the loss function L, use the gradient descent method to iteratively update the model parameters until the loss function converges and the training is completed.

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

为模型第j层EMCNN中CNN衰减补偿模块输出PET图像中第i个像素点的浓度值，

为模型第j层EMCNN中EM重建模块输出PET图像中第i个像素点的浓度值。Among them: k ₁ and k ₂ are weight coefficients, N _b is the total number of pixels in the PET image, N is the number of samples in the training set, N _p is the total number of layers of EMCNN in the model, x _{out, i} is the model reconstruction output PET image The concentration value of the i-th pixel in x _{label, i} is the concentration value of the i-th pixel in the label x _AC ,

Output the concentration value of the ith pixel in the PET image for the CNN attenuation compensation module in the jth layer EMCNN of the model,

Output the concentration value of the ith pixel in the PET image for the EM reconstruction module in the jth layer EMCNN of the model.

The present invention realizes the process of directly reconstructing PET images based on measurement data without attenuation correction, and constructs a network framework based on EM reconstruction and CNN, EM is used to reconstruct rough PET images, CNN is used to improve the quality of PET images, and CNN can learn The attenuation mechanism between the attenuation-corrected measurement data and the PET image realizes attenuation compensation for the PET image. The present invention can realize the mapping from sinogram _NAC to PET image without additional CT or MR scanning and attenuation correction for measurement data. In addition, the present invention has fast convergence in the training phase, can quickly obtain the training model, and can quickly obtain the PET image based on the measurement data after the model training is completed.

Description of drawings

Fig. 1 is a schematic flow chart of the PET reconstruction method of the present invention.

Fig. 2 is a schematic diagram of the processing flow of sinogram measurement data in the present invention.

Fig. 3 is a schematic diagram of the overall structure of the PET reconstruction model of the present invention.

Fig. 4 is a schematic diagram of the comparison of reconstruction results between the model EMCNN of the present invention and the existing model DeepPET.

detailed description

In order to describe the present invention more specifically, the technical solutions of the present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

As shown in Figure 1, the non-attenuation correction PET reconstruction method based on the maximum expectation network in the present invention is divided into two stages as a whole:

training phase

(1) Anesthetize and inject 1mCi radioactive tracer ( ¹⁸ F-FDG) to 12 rats with glioma, and then immediately perform a 60-minute dynamic scan on the Siemens Micro-PET/CT Inveon instrument to obtain measurements Data Three-dimensional (3D) sinogram. The detector of the PET system has 128 detection units and 160 angles, and the sampling protocol is set to 3×60s, 9×180s, 6×300s.

与PET图像x有如下映射关系：PET scan data can be modeled as a collection of independent Poisson random variables with mean

It has the following mapping relationship with PET image x:

Among them: y represents the measurement data, G represents the system matrix of the PET system, x represents the PET image to be reconstructed, and u represents the noise.

(2) Collect CT images of 12 rats, and convert the CT images into attenuation coefficients at 511KeV energy to obtain attenuation maps.

(3) Perform random correction, normalization correction, dead time correction, scattering correction, and attenuation correction on the sinogram in step (1) in order to obtain 3D sinogram _AC . The correction process is shown in Figure 2. In order to verify that the model EMCNN of the present invention can achieve attenuation compensation for PET images during the PET reconstruction process, it is necessary to obtain a set of unattenuated measurement data sinogram _NAC , sinogram _NAC undergoes random correction, normalization correction, dead time correction and scatter correction .

(4) Reconstruct sinogram _AC into AC PET image based on OSEM-map. 3D sinogram _AC can be reconstructed into 3D PET images of 18 time frames, each frame contains 159 slices, and the size of the image is 128×128. Due to the large size of rats and only one scanning bed, only the brain and abdomen of rats with more detection targets are scanned, so some of the 159 slice images in each frame are "empty" images, and the final true size The mouse PET images are 2000 two-dimensional (2D) PET images randomly generated by excluding the "empty" images from the above 3D images. Therefore, the rat data contains 2000 pairs of AC PET images-sinogram _AC and 2000 pairs of AC PET images-sinogram _NAC .

(5) Use sinogram _NAC and sinogram _AC as the input training network model of the network respectively (the training model based on sinogram _AC is used as a control experiment to verify the attenuation compensation ability of the maximum expected network), the overall structure of the network model is shown in Figure 3 Shown, including initialization module, EM reconstruction module and CNN optimization module, where:

The initialization module uses the initialization matrix to convert the measurement data into an initialization image x ⁽⁰⁾ , the dimension of the input data is batch size×20480, and the dimension of the output data is batch size×16384. The initialization process depends on the calculation of the initial matrix, and the calculation formula of the initial matrix is:

Among them, Q _init represents the initial matrix, x and y represent the PET image of the training data and the measurement data, respectively, λ is the regularization coefficient, and I is the identity matrix.

The EM reconstruction module reconstructs the initialization image into a PET image x ⁽¹⁾ , and since the sinogram _NAC has not undergone attenuation correction, the PET image reconstructed by EM is inaccurate. x ^{(1) is} then optimized by CNN, which learns the attenuation mechanism between sinogram _NAC and AC PET images, and realizes attenuation compensation for PET images.

EM reconstruction solves the following optimization problems:

为测量数据y和均值

的泊松负log似然表达，β为正则化系数，k为迭代次数，r^(k-1)为第k-1迭代输出的图像。in:

is the measured data y and the mean

The Poisson negative log likelihood expression of , β is the regularization coefficient, k is the number of iterations, and r ^(k-1) is the image output by the k-1th iteration.

This optimization problem has the following variants:

The EM reconstruction problem is equivalent to finding the root of the above formula Q _j (x _j ), and the root of Q _j (x _j ) has the following form:

g_ij代表是系统矩阵G中第i行第j列的元素，n_d代表发射光线的数量，n_p代表PET图像的像素数，

Among them: k represents the number of iterations,

g _ij represents the element of row i and column j in the system matrix G, n _d represents the number of emitted rays, n _p represents the number of pixels of the PET image,

The CNN module has a symmetrical structure, which consists of 4 convolutional layers, 2 batch normalization layers, 2 activation layers and 1 soft threshold layer. The convolution kernel size of each convolutional layer is 3×3, and the depths of the four convolutional layers from input to output are 32, 32, 32, and 1 in sequence.

The PET image x ⁽¹⁾ output by EM reconstruction is used as the input of CNN, and the convolution kernel learns the spatial characteristics of the image; the activation layer enhances the nonlinearity of the network and improves the fitting ability of the network; the batch normalization layer is conducive to the rapid convergence of the network ; The soft threshold layer enhances the sparsity of the data, and the symmetric structure before and after the soft threshold improves the image reconstruction performance. The complete reconstruction model contains a multi-layer EM-CNN structure. In order to limit the background value of the PET image, a ReLU layer is passed before the final output, and the attenuation-compensated PET image is finally output.

(6) The sinogram is used as the input of the network, and the AC PET image is used as the label. After the sinogram is input to the network, the loss function between the network output result and the true value must be calculated at the end of each forward operation. The calculated loss function will be in Backpropagation in the network, update the parameters of neurons layer by layer during the propagation process, repeat the above process until the loss value is less than a certain value or the training period reaches the set value, and save the training model.

The expression of the loss function L is as follows:

和

分别为第j层CNN输出图像和第j层EM输出图像中第i像素点的浓度值。Among them, N _b , N and N _p respectively represent the number of pixels of the PET image, the total number of images in the training set and the number of convolution modules in the CNN, k ₁ and k ₂ are the weight coefficients, x _out,i and x _label,i are the concentration values of the i-th pixel in the final output image of EMCNN and the true value label, respectively,

with

are the concentration values of the i-th pixel in the j-th layer CNN output image and the j-th layer EM output image, respectively.

(7) The reconstruction model EMCNN of the present invention is implemented using Pytorch 1.2.0, and is trained on an Ubuntu 18.04LTS server with TITAN RTX. The Adam optimizer is used for network update, and its initial learning rate is 0.001. During the training process, every 20 training cycle, the learning rate is reduced to half of the original, the batch size is 16, the number of layers of EM-CNN in the network is 3, the training cycle is 120, and k ₁ : k ₂ = 100:1 in the loss function, each completed The verification set is reconstructed once in 5 training cycles and the training model is saved.

inference stage

(1) Anesthetize and inject 1mCi radioactive tracer ( ¹⁸ F-FDG) to 12 rats with glioma, and then immediately perform a 60-minute dynamic scan on the Siemens Micro-PET/CT Inveon instrument to obtain measurements Data 3D sinogram. The detector of the PET system has 128 detection units and 160 angles, and the sampling protocol is set to 3×60s, 9×180s, 6×300s.

(2) Collect CT images of 12 rats, and convert the CT images into attenuation coefficients at 511KeV energy to obtain attenuation maps.

(3) Perform random correction, normalization correction, dead time correction, scatter correction and attenuation correction on the sinogram in step (1) in sequence to obtain a 3D sinogram _AC , as shown in Figure 2 .

(4) Input the sinogram _NAC of the test sample into the trained network model to obtain the PET reconstruction image.

(5) Evaluate network reconstruction performance based on PSNR, SSIM and absolute error indicators.

In the following, we conduct experiments based on rat data to verify the effectiveness of this embodiment.

A total of 4000 sets of data were generated in this experiment, 3600 sets of data were used for training, and 400 sets were divided into two non-overlapping parts for verification and testing respectively. We evaluate EMCNN based on PSNR, SSIM, and absolute error metrics and compare it with the DeepPET method, both of which use the best-performing model on the validation set to reconstruct the test set.

The PET reconstructed image based on the model EMCNN of the present invention is shown in Figure 4, the first behavior is the reconstructed image, and the second behavior is the error graph; no matter it is sinogram _NAC or sinogram _AC , the reconstructed image not only has the distribution profile of the overall radioactivity concentration close to the true value, but also The capture of details is also very precise, and the two highlighted areas in the real value are also well restored, and the reconstructed images based on sinogram _NAC and sinogram _AC are almost the same. In contrast to the reconstruction results based on DeepPET, the distribution profile of the overall radioactivity concentration in the reconstructed images based on sinogram _NAC and sinogram _AC is relatively similar to the true value, but both of them are almost missing all the details, and the reconstructed image based on sinogram _AC can barely distinguish a highlight area, but another highlight area is missing, and the reconstructed image based on sinogram _NAC is missing all highlight details. The same conclusion can be obtained by observing the error map. The reconstructed image based on EMCNN has fewer pixels with errors, and the average error value is small (0.005); while the reconstructed image based on DeepPET has more pixels with errors, and most of the error values Greater than 0.005.

The mean and standard deviation of PSNR, SSIM and absolute error of reconstructed images based on EMCNN and DeepPET are recorded in Table 1. The PSNR index of the EMCNN method for the two sets of data with or without attenuation correction has reached a good level and the two are equivalent (sinogram _NAC : 35.89, sinogram _AC : 35.86), and it is also much higher than the PSNR of DeepPET; while the image reconstructed based on DeepPET In , the PSNR of the attenuation-corrected image is higher than that of the non-attenuation-corrected image (sinogram _NAC : 29.20, sinogram _AC : 30.58).

Table 1

The above indicators show that EMCNN can better reconstruct image details while maintaining similar structure. The SSIM indicator shows the structural difference between the reconstructed image and the original image. EMCNN can better maintain the overall structure of the image. Experimental results show that the present invention has advantages in solving PET reconstruction without attenuation correction.

The above description of the embodiments is for those of ordinary skill in the art to understand and apply the present invention. It is obvious that those skilled in the art can easily make various modifications to the above-mentioned embodiments, and apply the general principles described here to other embodiments without creative efforts. Therefore, the present invention is not limited to the above embodiments, and improvements and modifications made by those skilled in the art according to the disclosure of the present invention should fall within the protection scope of the present invention.

Claims (8)

1. A PET reconstruction method without attenuation correction based on the maximum expectation network, comprising the steps of: (1) Utilize the PET system to scan the biological tissue injected with the radioactive tracer to collect and obtain the measurement data sinogram _NAC ; (2) Perform CT or MR acquisition on the biological tissue injected with radioactive tracer, and then convert the value in the CT or MR image into the attenuation coefficient at 511KeV energy, so as to generate the attenuation map; (3) correcting the measurement data sinogram _NAC by using the attenuation map to obtain the corrected measurement data sinogram _AC ; (4) performing PET reconstruction based on the measurement data sinogram _AC , and obtaining the corresponding PET image x _AC ; (5) Perform multiple scans and reconstructions according to steps (1) to (4) to obtain a large number of samples, each group of samples contains corresponding sinogram _NAC and x _AC , and then divide all samples into training set and test set; (6) Build a PET reconstruction model based on the maximum expectation network, which includes an initialization module, an EM reconstruction module, and a CNN attenuation compensation module, wherein the initialization module uses the initialization matrix to convert the measurement data sinogram _NAC into an initialization image x ⁽⁰⁾ , and the EM reconstruction module Used to reconstruct the initialization image x ⁽⁰⁾ into a PET image r ⁽¹⁾ , the CNN attenuation compensation module is used to perform attenuation compensation on the PET image r ⁽¹⁾ to obtain the PET image x ⁽¹⁾ output by the first layer iteration, and The EM reconstruction module and the CNN attenuation compensation module are combined as an optimized structure EMCNN and repeated multi-layer iterations, x ⁽¹⁾ is used as the input of the second layer EMCNN, and after multi-layer iterations, the PET image reconstructed by the model is finally output; (7) Use the sinogram _NAC in the training set sample as the model input, and x _AC as the label to train the PET reconstruction model; (8) Input the sinogram _NAC in the test set sample into the trained PET reconstruction model, and the corresponding PET image can be directly reconstructed without attenuation correction. 2. The non-attenuation correction PET reconstruction method according to claim 1, characterized in that: the scanning mode of the PET system in the step (1) can be static scanning or dynamic scanning. 3. The non-attenuation correction PET reconstruction method according to claim 1, characterized in that: in the step (2), the value in the CT or MR image is converted into the attenuation coefficient under 511KeV energy, which can be scaled, segmented or Method implementation for scaling segmented blending. 4. The PET reconstruction method without attenuation correction according to claim 1, characterized in that: in the step (3), correcting the measurement data sinogram _NAC includes random correction, normalization correction, dead time correction, scatter correction and Attenuation correction. 5. The PET reconstruction method without attenuation correction according to claim 1, characterized in that: the initialization matrix expression used by the initialization module is as follows: Q _init ＝xy ^T (yy ^T +λI) ^-1 Among them: Q _init is the initialization matrix, x and y are the x _AC and sinogram _NAC in the training set samples respectively, λ is the regularization coefficient, I is the identity matrix, and ^T is the transpose. 6. The PET reconstruction method without attenuation correction according to claim 1, wherein the CNN attenuation compensation module consists of a convolutional layer D1, a batch normalization layer B1, a ReLU activation layer R1, and a convolutional layer from input to output. Layer D2, soft threshold calculation layer, convolutional layer D3, ReLU activation layer R2, batch normalization layer B2, and convolutional layer D4 are sequentially connected, and the convolution kernels in the four convolutional layers D1~D4 are all 3×3, the depth is 32, 32, 32, 1 in turn. 7. non-attenuation correction PET reconstruction method according to claim 1, is characterized in that: further, in described step (7), the process that PET reconstruction model is trained is as follows: 6.1 Initialize the model parameters, including the bias vector and weight matrix of each layer, learning rate, optimization method and maximum number of iterations; 6.2 Input the measurement data sinogram _NAC in the training set sample to the model, and the model forward propagates and outputs the reconstructed PET image, and calculates the loss function L between the PET image and the label x _AC ; 6.3 According to the loss function L, use the gradient descent method to iteratively update the model parameters until the loss function converges and the training is completed. 8. The PET reconstruction method without attenuation correction according to claim 7, characterized in that: the expression of the loss function L is as follows:

Among them: k ₁ and k ₂ are weight coefficients, N _b is the total number of pixels in the PET image, N is the number of samples in the training set, N _p is the total number of layers of EMCNN in the model, x _{out, i} is the model reconstruction output PET image The concentration value of the i-th pixel in x _{label, i} is the concentration value of the i-th pixel in the label x _AC ,

Output the concentration value of the ith pixel in the PET image for the CNN attenuation compensation module in the jth layer EMCNN of the model,

Output the concentration value of the ith pixel in the PET image for the EM reconstruction module in the jth layer EMCNN of the model.

Images