A maximum likelihood expectation network based unattenuated correction PET reconstruction method

Abstract

The application discloses a PET reconstruction method based on a maximum expectation network, and realizes a process of directly reconstructing a PET image based on non-attenuation correction measurement data. NAC The application does not need additional CT or MR scanning, and does not need to correct the measurement data for attenuation, so that the mapping from sinogram to PET image can be realized. In addition, the application converges fast in the training stage, can quickly obtain a training model, and can quickly obtain a PET image based on measurement data after the model training is completed.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of biomedical image reconstruction, and particularly relates to a maximum expectation network-based PET reconstruction method without attenuation correction. BACKGROUND

[0002] As a medical imaging tool for cancer diagnosis, brain function imaging and treatment recovery monitoring, PET (positron emission computed tomography) can realize non-invasive molecular level information capture of specific targets. Radioactive tracers usually enter the biological body through intravenous injection, nasal inhalation and the like and participate in the physiological metabolic reaction of the biological body for a period of time. The nuclide of the radioactive tracer emits a positron which occurs annihilation reaction with surrounding negative electrons to generate a photon. A detector records the space-time information of the photon to reconstruct the spatial distribution of the tracer.

[0003] In recent years, the rapid development of PET quantitative image reconstruction technology makes it widely used in the field of tissue and organ pathological diagnosis, protein biomolecule quantitative analysis, drug development, etc. The dependence of each field on quantitative PET image in turn promotes the research of improving the accuracy of PET quantification. 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] introduces and estimates a quantitative coefficient in the forward model of PET measurement data to obtain quantitative results. Literature [Joel S. Karp, Suleman Surti, Margaret E. Daube-Witherspoon, Gerd Muehllehner Journal of Nuclear Medicine Mar 2008, 49(3) 462-470] attempts to use time-of-flight (TOF) information to improve the signal-to-noise ratio of the reconstructed image, and proves 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 of time-of-flight on PET tumor detection. J Nucl Med. 2009 Aug; 50(8): 1315-23] uses the fast detection of TOF to improve the accuracy of photon positioning of the response line (LOR) to improve the quality of PET reconstructed image; some studies focus on introducing point spread function (PSF) in the forward modeling of PET imaging, because PSF can reflect the effect of photon interaction with the biological body, so it can correct the physical effects such as attenuation, scattering, and improve the quantitative accuracy of image reconstruction. However, the quality of PET image reconstruction is still limited by many factors such as imaging physical effects, tracer kinetics, and motion of the measured object or equipment, among which photon attenuation as an unavoidable physical effect of PET measurement data acquisition seriously affects the accuracy of PET image.

[0004] Attenuation correction based on CT or MRI anatomical information in PET / CT or PET / MR imaging systems is currently a common correction method, but in some cases, the information provided by CT or MRI is inaccurate or cannot be obtained at all. For example, in PET / CT and PET / MR, the regions affected by respiratory and cardiac motion, the regions affected by metal implants in PET / CT and PET / MR, and all regions that are challenging for reliable attenuation correction based on MR (e.g. lung), respiratory and cardiac motion often cause mismatches between CT-derived attenuation and tracer activity distribution. In PET / MR, many MR sequences are usually applied, so most of the PET data are not acquired simultaneously with the MR images for attenuation correction; in PET / CT, attenuation and activity images are never acquired simultaneously. Therefore, any patient motion after CT or MR acquisition will destroy the attenuation image; if the data source for attenuation correction is inaccurate, quantitative analysis of PET cannot be performed, so there is an urgent need for a method of quantitative PET reconstruction without attenuation correction. SUMMARY

[0005] In view of the above, the present application provides a maximum expectation network-based attenuation-free PET reconstruction method, which combines the maximum expectation algorithm and the convolutional neural network (CNN) to realize the reconstruction and attenuation compensation of the PET image.

[0006] A maximum expectation network-based attenuation-free PET reconstruction method, comprising the following steps:

[0007] (1) Scanning a biological tissue injected with a radioactive tracer using a PET system to obtain measurement data sinogram NAC ;

[0008] (2) CT or MR acquisition of the biological tissue injected with the radioactive tracer, and then converting the values in the CT or MR image into attenuation coefficients at 511 KeV energy to generate an attenuation map;

[0009] (3) Correcting the measurement data sinogram NAC using the attenuation map to obtain corrected measurement data sinogram AC ;

[0010] (4) PET reconstruction based on the measurement data sinogram AC to obtain the corresponding PET image x AC ;

[0011] (5) Performing multiple scan reconstructions according to steps (1) to (4) to obtain a large number of samples, each set of samples containing corresponding sinogram NAC and x AC, and then all samples are divided into a training set and a test set;

[0012] (6) constructing a PET reconstruction model based on a maximum expectation network, including an initialization module, an EM reconstruction module, and a CNN attenuation compensation module, wherein the initialization module converts measured data sinogram NAC into an initial image x (0) using an initialization matrix, the EM reconstruction module is used to reconstruct the initial 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 a PET image x (1) of a first layer iteration output, and the EM reconstruction module and the CNN attenuation compensation module are combined as an optimization structure EMCNN and repeated for multiple layer iterations, x (1) is taken as an input of a second layer EMCNN, and a PET image finally output by the model reconstruction is obtained after multiple layer iterations;

[0013] (7) taking sinogram NAC in the training set sample as a model input, and taking x AC as a label, the PET reconstruction model is trained;

[0014] (8) inputting sinogram NAC in the test set sample into the trained PET reconstruction model, and directly reconstructing a corresponding PET image without attenuation correction.

[0015] Further, the scanning mode of the PET system in the step (1) can be static scanning or dynamic scanning.

[0016] Further, the conversion of the numerical value in the CT or MR image into the attenuation coefficient under the 511KeV energy can be realized by using a scaling method, a segmentation method, or a scaling and segmentation hybrid method.

[0017] Further, the correction of the measured data sinogram NAC in the step (3) includes random correction, normalization correction, dead time correction, scattering correction, and attenuation correction.

[0018] Further, the initialization matrix used by the initialization module has the following expression:

[0019] Q init = xy T (yy T + λI) -1

[0020] wherein: Q initTo initialize the matrix, x and y are the x AC and sinogram NAC , λ is the regularization coefficient, I is the identity matrix, T denotes the transpose.

[0021] Further, the CNN attenuation compensation module is sequentially connected by 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, a ReLU activation layer R2, a batch normalization layer B2, and a convolutional layer D4 from input to output, wherein the convolutional kernel size of the four convolutional layers D1-D4 is 3x3, and the depth is 32, 32, 32, and 1, respectively.

[0022] Further, the process of training the PET reconstruction model in step (7) is as follows:

[0023] 6.1 Initialize the model parameters, including the bias vector and weight matrix of each layer, the learning rate, the optimization method, and the maximum number of iterations;

[0024] 6.2 Input the measured data sinogram NAC in the training set sample into the model, and the model forward propagates to output the reconstructed PET image, and calculates the loss function L between the PET image and the label x AC ;

[0025] 6.3 According to the loss function L, the model parameters are continuously updated by gradient descent method until the loss function converges, and the training is completed.

[0026] Further, the expression of the loss function L is as follows:

[0027]

[0028] where: k1 and k2 are weight coefficients, N b is the total number of pixels of the PET image, N is the number of samples in the training set, N p is the total number of layers of the EMCNN in the model, x out,i is the concentration value of the i-th pixel point in the model reconstructed output PET image, x label,i is the concentration value of the i-th pixel point in the label x AC , is the concentration value of the i-th pixel point in the PET image output by the CNN attenuation compensation module in the j-th layer EMCNN in the model, is the concentration value of the i-th pixel point in the PET image output by the EM reconstruction module in the j-th layer EMCNN in the model.

[0029] This invention realizes the process of directly reconstructing PET images based on measurement data without attenuation correction. It constructs a network framework based on EM reconstruction and CNN. EM is used to reconstruct coarse PET images, while CNN is used to improve PET image quality. CNN can learn the attenuation mechanism between measurement data without attenuation correction and PET images, achieving attenuation compensation for PET images. This invention does not require additional CT or MR scans, nor does it require attenuation correction of the measurement data, to achieve reconstruction from sinogram... NAC The invention maps images to PET images. Furthermore, it exhibits fast convergence during the training phase, enabling rapid acquisition of the trained model, and after model training is complete, it can quickly obtain PET images based on measurement data. Attached Figure Description

[0030] Figure 1 This is a schematic flowchart of the PET reconstruction method of the present invention.

[0031] Figure 2 This is a schematic diagram of the processing flow of sinogram measurement data in this invention.

[0032] Figure 3 This is a schematic diagram of the overall structure of the PET reconstruction model of the present invention.

[0033] Figure 4 This is a schematic diagram comparing the reconstruction results of the EMCNN model of this invention with the existing model DeepPET. Detailed Implementation

[0034] 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.

[0035] like Figure 1 As shown, the present invention, based on the attenuation-free PET reconstruction method using a maximum expectation network, is divided into two stages:

[0036] Training phase

[0037] (1) Twelve rats with glioma were anesthetized and injected with 1 mCi of radioactive tracer. 18 The F-FDG was then immediately followed by a 60-minute dynamic scan on a Siemens Micro-PET / CT Inveon instrument to obtain the measurement data in three-dimensional (3D) sinogram. The PET system's detector has 128 detector units, 160 angles, and sampling protocols set to 3×60s, 9×180s, and 6×300s.

[0038] PET scan data can be modeled as a set of independent Poisson random variables, with the mean... The following mapping relationship exists between the image and the PET image x:

[0039]

[0040]

[0041] where: y represents the measured data, G represents the system matrix of the PET system, x represents the PET image to be reconstructed, and u represents the noise.

[0042] (2) CT image acquisition was performed on 12 rats, and the CT image was converted into an attenuation coefficient at 511 KeV energy to obtain an attenuation map.

[0043] (3) The sinogram of step (1) was sequentially subjected to random correction, normalization correction, dead time correction, scatter correction and attenuation correction to obtain a 3D sinogram AC , and the correction process is shown in Figure 2 . In order to verify that the model EMCNN of the present application can realize attenuation compensation of the PET image in the PET reconstruction process, a group of measured data sinogram NAC without attenuation is required, and the sinogram NAC is subjected to random correction, normalization correction, dead time correction and scatter correction.

[0044] (4) The sinogram AC is reconstructed into an AC PET image based on OSEM-map. The 3D sinogram AC can be reconstructed into a 3D PET image of 18 time frames, each frame containing 159 slices, and the size of the picture is 128x128. Since the rat is large in volume and has only one scanning bed, only the brain and abdomen of the rat with more detection targets are scanned, so part of the 159 slice images in each frame is "empty" image, and the final real rat PET image is 2000 two-dimensional (2D) PET images generated by randomly shuffling the 3D images after removing the "empty" images. Therefore, the rat data contains 2000 pairs of AC PET images-sinogram AC and 2000 pairs of AC PET images-sinogram NAC .

[0045] (5) The sinogram NAC and the sinogram AC are used as the input of the network to train the network model (the sinogram AC based model is used as a control experiment to verify the attenuation compensation ability of the maximum expectation network), and the overall structure of the network model is shown in Figure 3 , which includes an initialization module, an EM reconstruction module and a CNN optimization module, wherein:

[0046] The initialization module converts the measurement data into an initialization image x using an initialization matrix (0) , the dimension of the input data is batch size x 20480, and the dimension of the output data is batch size x 16384. The initialization process relies on the calculation of an initial matrix, whose formula is:

[0047]

[0048] where Q init represents the initial matrix, x and y represent the PET image and the measurement data of the training data respectively, λ is a regularization coefficient, and I is an identity matrix.

[0049] The EM reconstruction module reconstructs the initialization image into a PET image x (1) Since the sinogram NAC is not corrected for attenuation, the PET image reconstructed by EM is not accurate. x (1) is then optimized by a CNN, which learns the attenuation mechanism between the sinogram NAC and the AC PET image and realizes attenuation compensation for the PET image.

[0050] The EM reconstruction solves the following optimization problem:

[0051]

[0052]

[0053] where: is the Poisson negative log-likelihood expression of the measurement data y and the mean , β is a regularization coefficient, k is the number of iterations, and r (k-1) is the image output in the k-1 iteration.

[0054] The optimization problem has the following transformation:

[0055]

[0056]

[0057] 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:

[0058]

[0059] where: k represents the number of iterations, g ijrepresents the element of the i-th row and j-th column in the system matrix G, n d represents the number of emitted light rays, n p represents the number of pixels of the PET image,

[0060] The CNN module has a symmetrical structure, which is composed of 4 convolutional layers, 2 batch normalization layers, 2 activation layers and 1 soft threshold layer in total. The size of the convolution kernel of each convolutional layer is 3x3, and the depth of the four convolutional layers from input to output is 32, 32, 32, 1 in turn.

[0061] The PET image x output by EM reconstruction (1) As the input of the CNN, the convolution kernel learns the spatial features 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 symmetrical structure before and after the soft threshold improves the reconstruction performance of the image. The complete reconstruction model contains multiple layers of EM-CNN structure, in order to limit the background value of the PET image, a ReLU layer is added before the final output, and the final output is the PET image after attenuation compensation.

[0062] (6) The sinogram is taken as the input of the network, and the AC PET image is taken as the label. After the sinogram is input into the network, the loss function between the network output result and the true value is calculated at the end of each forward operation. The calculated loss function will be back propagated in the network, and the parameters of the neurons will be updated layer by layer in the propagation process. The above process is repeated until the loss value is less than a certain value or the training period reaches a set value, and the trained model is saved.

[0063] The expression of the loss function L is as follows:

[0064]

[0065]

[0066] wherein, N b , N and N p 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 respectively, k1 and k2 are weight coefficients, x out,i and x label,i are the concentration values of the i-th pixel point in the final output image of the EM CNN and the true value label respectively, and are the concentration values of the i-th pixel point in the j-th layer CNN output image and the j-th layer EM output image respectively.

[0067] (7) The reconstruction model EMCNN of this invention is implemented using PyTorch 1.2.0 and trained on an Ubuntu 18.04LTS server with TITAN RTX. The network update uses the Adam optimizer with an initial learning rate of 0.001. During training, the learning rate is reduced to half of its original value every 20 training epochs. The batch size is 16, the number of layers in the EM-CNN network is 3, the training epochs are 120, and the loss function is k1:k2 = 100:1. The validation set is reconstructed and the training model is saved every 5 training epochs.

[0068] Inference phase

[0069] (1) Twelve rats with glioma were anesthetized and injected with 1 mCi of radioactive tracer. 18 The 3D sinogram (F-FDG) was then immediately performed on a Siemens Micro-PET / CT Inveon instrument for 60 minutes to obtain measurement data. The PET system's detector has 128 detector units, 160 angles, and sampling protocols set to 3×60s, 9×180s, and 6×300s.

[0070] (2) CT images were acquired from 12 rats and the CT images were converted into attenuation coefficients at 511 keV energy to obtain attenuation maps.

[0071] (3) Perform random correction, normalization correction, dead time correction, scattering correction, and attenuation correction on the sinogram from step (1) in sequence to obtain the 3D sinogram. AC ,like Figure 2 As shown.

[0072] (4) The sinogram of the test sample NAC The image is input into a pre-trained network model to obtain a PET reconstructed image.

[0073] (5) Evaluate network reconstruction performance based on PSNR, SSIM and absolute error metrics.

[0074] The following experiments, based on rat data, verify the effectiveness of this implementation method.

[0075] This experiment generated a total of 4000 datasets. 3600 datasets were used for training, and the remaining 400 datasets were divided into two non-overlapping parts for validation and testing, respectively. We evaluated EMCNN based on PSNR, SSIM, and absolute error metrics, and compared it with the DeepPET method. Both methods used the model that performed best on the validation set to reconstruct the test set.

[0076] The PET reconstructed images based on the model EMCNN of the application are shown in Fig. 6, where the first row is the reconstructed images, and the second row is the error images. Figure 4 As shown in Fig. 6, the first row is the reconstructed images, and the second row is the error images. Whether the sinogram NAC or the sinogram AC , the reconstructed images not only have the distribution profile of the overall radioactivity concentration close to the true value, but also accurately capture the details, and the two highlighted areas in the true value are also well restored, and the reconstructed images based on the sinogram NAC and the sinogram AC are also almost the same. In contrast, the reconstructed results based on DeepPET, the reconstructed images based on the sinogram NAC and the sinogram AC have the distribution profile of the overall radioactivity concentration similar to the true value, but both almost lack all details, the reconstructed image based on the sinogram AC can barely distinguish one highlighted area, but the other highlighted area is missing, and the reconstructed image based on the sinogram NAC lacks all highlighted details. The same conclusion can be obtained by observing the error images, the reconstructed images based on EMCNN have fewer pixel points with errors, and the mean error is smaller (0.005); and the reconstructed images based on DeepPET have more pixel points with errors, and most of the error values are greater than 0.005.

[0077] The PSNR, SSIM and mean and standard deviation of absolute error of the reconstructed images based on EMCNN and DeepPET are recorded in Table 1. The PSNR index of the EMCNN method for the two groups of data whether or not subjected to attenuation correction reaches a good level and is comparable (sinogram NAC : 35.89, sinogram AC : 35.86), and is also much higher than the PSNR of DeepPET; while in the images reconstructed based on DeepPET, the PSNR of the image subjected to attenuation correction is higher than that of the image not subjected to attenuation correction (sinogram NAC : 29.20, sinogram AC : 30.58).

[0078] Table 1

[0079]

[0080] The above indexes show that EMCNN can better reconstruct image details while maintaining structural similarity, the SSIM index shows the difference in structure between the reconstructed image and the original image, and EMCNN can better maintain the overall structure of the image. The experimental results show that the application has an advantage in solving PET reconstruction without attenuation correction.

[0081] The foregoing description of the embodiments has been presented for the purpose of illustration and description. It is not intended to be exhaustive or to limit the application to the precise form disclosed. Modifications and variations are possible in light of the above teachings or can be acquired from practice of the application. As well, the application has been described above with the assistance of illustrative figures and detailed descriptions. It is obvious to a person skilled in the art that a variety of modifications and changes can be made without departing from the application disclosed in its broadest form.

Claims

1. A PET reconstruction method based on maximum likelihood network without attenuation correction, comprising the following steps: (1) Scanning of a biological tissue injected with a radioactive tracer by means of a PET system to acquire measurement data, a sinogram NAC ; (2) CT or MR acquisition is performed on biological tissue injected with radioactive tracers, and then the values in the CT or MR image are converted into attenuation coefficients at 511 KeV energy, thereby generating an attenuation map; (3) correcting the measurement data sinogram using the attenuation map to obtain a corrected measurement data sinogram NAC (3) correcting the measurement data sinogram using the attenuation map to obtain a corrected measurement data sinogram AC ; (4) Based on the measured data sinogram AC PET reconstruction is performed to obtain the corresponding PET image x AC ; (5) Perform multiple scan reconstruction according to steps (1)-(4) to get 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) constructing a PET reconstruction model based on a maximum expectation network, comprising an initialization module, an EM reconstruction module, and a CNN attenuation compensation module, wherein the initialization module uses an initialization matrix to convert measured data sinogram NAC into an initialization image x (0) , the EM reconstruction module is 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 a PET image x (1) of a first layer iteration output, and the EM reconstruction module and the CNN attenuation compensation module are combined as an optimization structure EMCNN and repeated for multiple layer iterations, x (1) serves as an input of a second layer EMCNN, and a PET image finally output by the model after multiple layer iterations is obtained through reconstruction; The initialization matrix expression used by the initialization module is as follows: Q init = xy T (yy T + λI) -1 wherein: Q init To initialize the matrix, x and y are the x AC and sinogram NAC , λ is the regularization coefficient, I is the identity matrix, T denotes the transpose; The CNN attenuation compensation module is sequentially connected by 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, a ReLU activation layer R2, a batch normalization layer B2, and a convolutional layer D4 from input to output, wherein the convolution kernel size in the four convolutional layers D1-D4 is 3*3, and the depth is 32, 32, 32, and 1 in sequence. (7) sinograms in the training set samples NAC As model input, x AC To train the PET reconstruction model as a label, the specific process is as follows: 7.1 Initialization of model parameters, including the bias vector and weight matrix of each layer, learning rate, optimization method, and maximum number of iterations; 7.2 The measured data in the training set samples sinogram NAC are input to the model, which forward propagates to output a reconstructed PET image, and the loss function L between this PET image and the label x AC is computed according to the following expression wherein: k1 and k2 are weight coefficients, respectively, N b is the total number of pixels of the PET image, N is the number of samples in the training set, N p is the total number of layers of the EMCNN in the model, x out,i is the concentration value of the i-th pixel point in the reconstructed output PET image of the model, x label,i is the label x AC is the concentration value of the i-th pixel point in the label x is the concentration value of the i-th pixel point in the PET image output by the CNN attenuation compensation module in the j-th layer EMCNN of the model, x is the concentration value of the i-th pixel point in the PET image output by the EM reconstruction module in the j-th layer EMCNN of the model. 7.3 According to the loss function L, the model parameters are continuously updated by gradient descent method until the loss function converges, and the training is completed. (8) The sinogram in the test set samples NAC By inputting the data into a trained PET reconstruction model, the corresponding PET image can be directly reconstructed without attenuation correction.

2. The attenuation-free correction PET reconstruction method of claim 1, wherein: The scanning mode of the PET system in the step (1) is static scanning or dynamic scanning.

3. The attenuation-free correction PET reconstruction method of claim 1, wherein: In the step (2), the values in the CT or MR image are converted into attenuation coefficients at 511 KeV energy by using a scaling, segmentation, or mixed scaling and segmentation method.

4. The attenuation-free correction PET reconstruction method of claim 1, wherein: The step (3) of correcting the measured data sinogram NAC includes random correction, normalization correction, dead-time correction, scatter correction, and attenuation correction.

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