A method for obtaining the radioactive activity distribution of PET and a PET system

Abstract

The present invention relates to a method for obtaining a PET radioactivity distribution and a PET system. The method includes: for detection data used for medical image reconstruction, obtaining a first PET image without attenuation correction and a second PET image with approximate attenuation correction of the detection data; according to a pre-constructed mapping from a PET prior image α to a linear attenuation coefficient image μ, and a known logarithmic likelihood function with unknowns being the PET radioactivity distribution x and the linear attenuation coefficient distribution μ, obtaining a logarithmic likelihood function with a constraint term, where the constraint term is the mapping from the PET prior image α to the linear attenuation coefficient image μ; using an iterative algorithm to maximize the logarithmic likelihood function of the constraint term, and when an end condition is reached, obtaining an estimated value of the PET radioactivity distribution x. The above method can ensure the rapid convergence of the iterative process and increase the stability, quantification and accuracy of the reconstruction algorithm.

Description

Technical Field

[0001] The present invention relates to the technical field of medical imaging, and particularly to a method for obtaining the radioactive activity distribution of a PET and a PET system. Background Art

[0002] Positron Emission Tomography (PET) is one of the most advanced clinical imaging techniques in the current field of nuclear medicine. The positrons emitted by the radionuclide annihilate with the electrons inside the human body, generating two photons with opposite directions and an energy of 511 keV. Before the photon pairs are acquired by the PET system, they will be attenuated in the human body. Compared with the inside of the object, the photon pair events on the human body surface have a higher detection efficiency. If this ray attenuation effect is not corrected, attenuation artifacts will occur in the reconstructed image, where the image of the human body edge is too bright and the image of the internal tissue is too dark. The PET system usually integrates other modality systems (such as CT, MRI, etc.) to obtain the anatomical structure imaging of the patient. On the one hand, it can accurately locate the radionuclide distribution, improving the accuracy of lesion localization; on the other hand, the corresponding tissue density distribution of the patient is obtained for attenuation correction in PET image reconstruction, and the accurate distribution of the radiopharmaceutical in the patient body can be obtained. The PET functional imaging and the anatomical structure imaging of other modalities will ultimately be fused on the same machine, combining the advantages of functional imaging and anatomical imaging, achieving the purpose of early detection of lesions and diagnosis of diseases, and having more advantages in the diagnosis and treatment guidance of tumors, heart, and brain diseases.

[0003] However, in multi-modal acquisition applications, sometimes the attenuation information matching the PET image cannot be accurately obtained, resulting in incorrect attenuation correction and ultimately obvious artifacts in the PET image. In order to accurately correct the attenuation artifacts and broaden the application scenarios of PET imaging, the key lies in whether the attenuation information can be directly extracted from the PET acquisition data without relying on other modality imaging. Existing algorithms need to go through multiple iterations to approximate the ideal value, which leads to too long iteration convergence operation time. Usually, higher-level computing resources (such as high-performance GPUs) are required, increasing the usage cost. In addition, the iterative algorithm cannot ensure that the calculation result converges to the global optimal solution, but may converge to a local optimal solution. To avoid this situation, many restrictions and protections need to be added to the iterative algorithm, and adjustment parameters also need to be set, which reduces the stability and robustness of the algorithm. Summary of the Invention

[0004] (1) Technical Problems to be Solved

[0005] In view of the above-mentioned disadvantages and deficiencies of the prior art, the present invention provides a method for obtaining the radioactive activity distribution of a PET and a PET system.

[0006] (2) Technical Solutions

[0007] To achieve the above object, the main technical solutions adopted by the present invention include:

[0008] In a first aspect, an embodiment of the present invention provides a method for obtaining a PET radioactivity distribution, which includes:

[0009] S10. For the detection data used for medical image reconstruction, obtain a first PET image without attenuation correction and a second PET image with approximate attenuation correction of the detection data. The second PET image is an image reconstructed after attenuating and correcting the first PET image based on the empirical value of the linear attenuation correction coefficient of a specified region;

[0010] S20. According to the pre-constructed mapping from the PET prior image α to the linear attenuation coefficient image μ, and the known logarithmic likelihood function with unknowns being the PET radioactivity distribution x and the linear attenuation coefficient distribution μ, obtain a logarithmic likelihood function with a constraint term, where the constraint term is the mapping from the PET prior image α to the linear attenuation coefficient image μ;

[0011] The PET prior image α is the first PET image without attenuation correction and / or the second PET image with approximate attenuation correction; the unknowns in the logarithmic likelihood function with the constraint term are: x, μ, and the parameters of the mapping;

[0012] S30. According to the logarithmic likelihood function with the constraint term, use an iterative algorithm to maximize the logarithmic likelihood function of the constraint term. When the end condition is reached, obtain an estimated value of the PET radioactivity distribution x;

[0013] The initial values of x, μ, and the parameters of the mapping in the iterative algorithm for maximizing the logarithmic likelihood function of the constraint term are specified values.

[0014] The end condition of this embodiment is to iterate until the logarithmic likelihood function converges. In practical applications, the influence of iteration time and noise can be considered, and usually, a recommended iteration termination value is given based on experience.

[0015] Optionally, before S20, a mapping from the PET prior image α to the linear attenuation coefficient image μ is pre-constructed;

[0016] The mapping includes:

[0017] μ = f(θ|α) Formula (1)

[0018] f represents the mapping of the training model, θ represents the parameters of the mapping, and α represents the input of the training model.

[0019] Optionally, S20 includes:

[0020] For the known logarithmic likelihood function \(L\) and \(\mu = f(\theta|\alpha)\), the logarithmic likelihood function with a constraint term is obtained as follows:

[0021]

[0022] where \(\rho\) is a hyperparameter used to adjust the weight between the logarithmic likelihood function and the learning network penalty term, \(\Delta\mu\) is the change step of the linear attenuation coefficient image \(\mu\), \(x\) represents the PET radioactivity distribution, and \(y\) represents the detection data.

[0023] Optionally, for formula (2), an alternating strategy is adopted based on a known solution algorithm to maximize the logarithmic likelihood function \(L\) with a constraint term ρ , and the estimated value of \(x\) that satisfies the maximized logarithmic likelihood function \(L\) with a constraint term ρ is obtained as the output value;

[0024] where the alternating iteration strategy includes: only updating one variable and fixing the other two variables at each step during the iteration, and repeating the update alternately in this way;

[0025] Specifically, the mapping parameter \(\theta\) is the initial value for accelerating the convergence speed pre-trained by a CNN network, Unet network, or GAN network as the training model;

[0026] The initial value of the attenuation coefficient distribution \(\mu\) is 0 or the second image of approximate attenuation correction

[0027] The initial value of the PET radioactivity distribution \(x\) is a set value; that is, the value of the all-space normal constant distribution / the pixel value of the all-space is 1000;

[0028] The known solution algorithm is MLEM, OSEM, or MAP.

[0029] In this embodiment, in order to accelerate the convergence speed, pre-training of the network can be performed first to generate general network parameters as the initial value of network parameter iteration, and then fine-tuning can be performed for a specific scanned patient.

[0030] The above pre-training can be understood as using a large amount of training data to train the model to complete the mapping from the prior PET image to the linear attenuation coefficient image. The pre-trained network parameters can be used as the starting value of the network fine-tuning process, making the model converge faster.

[0031] Optionally, for formula (2), keeping the PET radioactivity distribution \(x\) as a constant, the logarithmic likelihood function \(L\) with a constraint term is maximized for the unknown attenuation coefficient distribution \(\mu\) and the mapping parameter \(\theta\) ρ , and it is solved using the alternating direction method of multipliers (ADMM) iterative algorithm, and the process is divided into the following three steps:

[0032]

[0033]

[0034]

[0035] Among them, n represents the current iteration number, and the n-th iteration satisfies the end condition (i.e., the recommended iteration termination value); when using the ADMM algorithm, the constrained optimization problem is decoupled into a network training sub-problem with the L2 norm as the loss function - corresponding to formula (8) and a sub-problem for solving μ with a penalty term - corresponding to formula (9).

[0036] Specifically, first keep the linear attenuation coefficient distribution μ and the step size increment Δμ unchanged, and update θ based on formula (8); then based on formula (9), keep θ and Δμ unchanged and iteratively update μ; based on formula (10), keep μ and θ unchanged and update Δμ, and iterate in this way to approximate the optimal solution.

[0037] Δμ is an intermediate variable added to solve for μ and θ, representing the change amount of μ. This change amount of μ comes from formula (2). Because when constructing the log-likelihood function, a separate constraint needs to be imposed on Δμ (i.e., the L2-Norm of Δμ) to ensure that the change amplitude of μ is not too large.

[0038] Optionally, when the medical image is a PET image, before S10, the method further includes:

[0039] S00. Obtain training samples for training the model based on the reconstructed medical image and the matching associated image;

[0040] Among them, each training sample includes: the reconstructed PET image / simulated PET image, the approximate linear attenuation correction coefficient corresponding to the PET image, the other modality image corresponding to the PET image, the other modality image is used to obtain the true linear attenuation correction coefficient, and the true linear attenuation correction coefficient is used to verify whether the trained model converges;

[0041] S01. Train the model based on the training samples to obtain the trained model;

[0042] In the trained model, the mapping parameter θ minimizes the value of the loss function Φ for optimizing the trained model.

[0043] Optionally, training the model based on the training samples includes:

[0044] Input the approximate linear attenuation correction coefficient of each training sample into the model to obtain an output, and compare the output with the true linear attenuation correction coefficient obtained from the other modality image in the training sample by means of the loss function Φ;

[0045] and / or

[0046] Input the reconstructed attenuation-free PET image of each training sample into the model to obtain an output, and compare the output with the true linear attenuation correction coefficient obtained from other modality images in the training sample by means of the loss function Φ;

[0047] and / or,

[0048] Sum the reconstructed attenuation-free PET image and the approximate linear attenuation correction coefficient of each training sample, input the summed image into the model to obtain an output, and compare the output with the true linear attenuation correction coefficient obtained from other modality images in the training sample by means of the loss function Φ;

[0049] The loss function Φ is one or more of the L1 norm, L2 norm, and KL divergence, and is used to scale the similarity between each output of the model in training and the true linear attenuation correction coefficient to which the output belongs.

[0050] In a second aspect, an embodiment of the present invention further provides a PET system, including: a memory and a processor; computer program instructions are stored in the memory, and the processor executes the computer program instructions stored in the memory to specifically execute the method described in any one of the first aspects above.

[0051] In a third aspect, an embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is run by a processor, it executes a method for obtaining a PET radioactivity distribution as described in any one of the first aspects.

[0052] (III) Beneficial effects

[0053] In order to improve the convergence speed and result stability of the linear attenuation coefficient iterative algorithm, in the embodiments of the present invention, a mapping that maps a PET prior image to a linear attenuation coefficient image can be pre-constructed, and the mapping parameters and the linear attenuation coefficient are jointly added to the iterative solution process of the maximum likelihood function L of the PET radioactivity distribution. The current algorithm uses a more accurate linear attenuation coefficient estimate as the starting point for iteration to optimize the convergence path and converge to the global optimal solution as soon as possible, increasing the stability, quantification, and accuracy of the algorithm.

[0054] Furthermore, a deep learning network mapping is used to adaptively obtain mapping parameters suitable for the current PET scan data, so as to obtain a more accurate linear attenuation coefficient image estimate and apply it to the maximum likelihood function L iterative optimization algorithm. Compared with the initial values used in the original algorithm (a uniformly linear attenuation coefficient image of the entire imaging field of view or a linear attenuation coefficient image converted from other modality images), it does not depend on other modality images, and at the same time can effectively optimize the convergence path and improve the reliability.

[0055] In addition, the attenuation information extracted by deep learning is derived from PET images, and there is no mismatch between multi-modal images, so motion and truncation artifacts can be avoided during the convergence adjustment process. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 FIG. is a schematic flow chart of a method for obtaining a PET radioactivity distribution according to an embodiment of the present invention;

[0057] Figure 2 (a) is a schematic diagram of a PET image without attenuation correction;

[0058] Figure 2 (b) is a schematic diagram of a PET image with approximate attenuation correction;

[0059] Figure 2 (c) is a schematic diagram of a PET image with attenuation correction using the method of the present invention;

[0060] Figure 2 (d) is a schematic diagram of the estimation result of the prior distribution of the linear attenuation coefficient obtained by using a deep learning network. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0061] In order to better explain the present invention for easy understanding, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0062] In the multi-modal acquisition applications of the prior art, sometimes it is impossible to accurately obtain the attenuation information matching the PET data, resulting in incorrect attenuation correction and additional artifacts on the PET image.

[0063] Specifically, it is described as follows:

[0064] First, during PET multi-modal imaging, there may be position misalignment between images of different modalities. During a long PET scan, the patient's body may move (for example, the arms, head, etc. will move during a long scan time), which will also cause the PET image and other modal images to be mismatched, resulting in obvious attenuation artifacts.

[0065] Secondly, there is a possibility of false positives. To exclude the possibility of false positives, an additional delayed scan is required, which increases the patient's X-ray radiation dose during the scan.

[0066] Furthermore, the scanning range of PET is usually larger than that of other modalities (such as CT or MRI). When scanning patients with a relatively large body weight, it is very likely that other modal imaging cannot provide a large enough imaging range, resulting in truncation of the attenuation image. The application of this incomplete attenuation information in PET attenuation correction will also generate attenuation artifacts.

[0067] Finally, the application conditions of other modalities also restrict the application of PET imaging. For example, patients with dentures or pacemakers cannot undergo MR examinations, which also affects the application of PET / MR. In addition, CT imaging requires extremely high radioactive protection requirements, while MR imaging requires strict nuclear magnetic resonance shielding. These all result in high scanning protection requirements for multimodal imaging and are not easy to promote.

[0068] In order to accurately correct attenuation artifacts and broaden the application scenarios of PET imaging, attenuation information is directly extracted from PET acquisition data without relying on other modality imaging. At the same time, the operation speed and result stability of the linear attenuation coefficient iterative algorithm are improved. The present invention provides a method for obtaining the PET radioactivity distribution by means of the information of the mapping from the PET image to the linear attenuation coefficient image. In this method, other modality images are not required, and the convergence can be accelerated, and the stability and robustness are ensured.

[0069] For a better understanding of the solutions of the embodiments of the present invention, some terms are explained as follows:

[0070] The PET reconstructed image is the PET radioactivity distribution / the PET radioactivity distribution image x;

[0071] The attenuation correction coefficient, the linear attenuation coefficient, the linear attenuation correction coefficient, the linear attenuation coefficient image, and the linear attenuation correction coefficient image all represent the same meaning, and different descriptions are adopted in different embodiments.

[0072] Embodiment 1

[0073] As Figure 1 shown, the embodiment of the present invention provides a method for obtaining the PET radioactivity distribution. The execution subject of the method in this embodiment can be a control device / electronic device for the method of obtaining the PET radioactivity distribution. This control device can be integrated in the acquisition device of the PET system or a separate computer processing device. A method for obtaining the PET radioactivity distribution includes the following steps:

[0074] S10. For the detection data used for medical image reconstruction, obtain the first PET image without attenuation correction and the second PET image with approximate attenuation correction of the detection data. The second PET image is an image reconstructed after attenuating and correcting the first PET image based on the empirical value of the linear attenuation correction coefficient of a specified region;

[0075] S20. According to the pre-constructed mapping from the PET prior image α to the linear attenuation coefficient image μ, and the known log-likelihood function with unknowns being the PET radioactivity distribution x and the linear attenuation coefficient distribution μ, obtain the log-likelihood function with a constraint term, where the constraint term is the mapping from the PET prior image α to the linear attenuation coefficient image μ;

[0076] The PET prior image α is the first PET image without attenuation correction and / or the second PET image with approximate attenuation correction; the unknowns in the log-likelihood function with the constraint term are: x, μ, and the parameters of the mapping;

[0077] S30. According to the log-likelihood function with the constraint term, use an iterative algorithm to maximize the log-likelihood function of the constraint term. When the end condition is reached, obtain the estimated value of the PET radioactivity distribution x;

[0078] The initial values of x, μ, and the parameters of the mapping in the iterative algorithm for maximizing the log-likelihood function of the constraint term are specified values.

[0079] In this embodiment, it can be iterated until the log-likelihood function converges. In specific applications, the final end condition can be determined by combining the iteration time and noise, and an empirical iteration termination value.

[0080] It can be understood that before the above step S20, the mapping from the PET prior image α to the linear attenuation coefficient image μ can be constructed first;

[0081] The mapping includes:

[0082] μ = f(θ|α) Formula (1)

[0083] f represents the mapping of the training model, θ represents the parameters of the mapping, and α represents the input of the training model.

[0084] The training model in this embodiment can be a CNN network, a Unet network, or a GAN network.

[0085] Compared with the traditional method of combining other modality images for PET reconstruction, the attenuation correction information in the PET reconstruction process of this embodiment comes from the PET data itself. Therefore, when the PET multimodality images do not match due to breathing, heartbeat, or patient movement, the image can still be attenuated corrected to eliminate image artifacts; if there are artifacts in the attenuation images obtained from other modalities (such as for PET / CT scan patients with a cardiac pacemaker or metal braces in the body, and there are obvious metal artifacts in the CT images), accurate attenuation correction can still be performed.

[0086] Embodiment Two

[0087] To better understand the method described in the above-mentioned Embodiment 1, the following two methods will be specifically instantiated and described in combination with formulas. The method of this embodiment ensures the rapid and stable convergence of the estimated value of the radioactivity distribution. The following method describes the training process and the usage process together. The specific steps of this method are as follows:

[0088] The following steps 01 to 03 are all existing steps, and this embodiment does not improve them.

[0089] The present invention proposes a method that uses a deep learning network to train network parameters / mapping parameters in real time during the iterative solution process of the linear attenuation coefficient, maps from the PET prior image to obtain an accurate estimated linear attenuation coefficient image, and is used to adjust the convergence path of the radioactivity distribution to ensure the rapid and stable convergence of the solution of the radioactivity distribution. The specific steps of this method are as follows:

[0090] Step 01: The PET acquisition process can be modeled by the following formula:

[0091]

[0092] In formula (1), y = [y 1t , y 2t , …, y it , …, y NT ' represents the detected data, i.e., the detection data. represents the average value of the detection data, N represents the size of the detection data sinogram, T represents the size of the discrete space of the time of flight TOF, i represents the variable index (index) of the line of response LOR (line of response) of the detection data sinogram, and t represents the variable index of the discrete space of the time of flight TOF. The superscript single quote represents the matrix transpose operation. x = [x1, x2, …, x j , …, x M ' represents the unknown radioactivity distribution image, M represents the size of the radioactivity distribution image space, j represents the variable index of the radioactivity distribution image space, and represents the point source at the corresponding spatial position. μ = [μ1, μ2, …, μ k , …, μ K ' represents the unknown linear attenuation coefficient image, K represents the size of the linear attenuation coefficient image space, k represents the variable index of the linear attenuation coefficient image space, and represents the point source at the corresponding spatial position. A = [A ijt is the system matrix, which mathematically expresses the probability that the point source j at the spatial position in the PET system is detected by the line of response LORi and the time of flight TOF is t, reflecting the physical characteristics of the system, l = [l ikis the linear attenuation coefficient matrix, representing the trajectory crossing length when the LOR i passes through the spatial position point source k. r = [r 1t , r 2t , …, r it , …, r NT ' represents the average value of random noise and scatter noise.

[0093] Step 02: The PET detection data follows a Poisson distribution, and the unknowns are the PET radioactivity distribution x and the linear attenuation coefficient distribution μ. Then the log-likelihood function of the detection data is expressed as:

[0094]

[0095] Step 03: Substitute formula (1) into formula (2), and ignoring the terms unrelated to the unknowns, the log-likelihood function can be written as:

[0096]

[0097] The above formula (3) is the log-likelihood function and also the objective function below.

[0098] Step 04: Construct a deep neural network to implement the mapping from the PET prior image α to the linear attenuation coefficient image μ:

[0099] μ = f(θ|α) (4)

[0100] The PET prior image α of the same patient is used as the input of the deep neural network, and the network parameters θ, i.e., the mapping parameters, are trained and updated during the problem optimization process.

[0101] The PET prior image α selected for the mapping input is the PET reconstruction image without attenuation correction At the same time, an approximate linear attenuation coefficient image conjecture is selected The approximate attenuation correction image obtained by performing attenuation correction

[0102] In the traditional reconstruction process, only the collected data is used. In this embodiment, the prior image is an additional image obtained for assisting reconstruction. In this embodiment, the PET reconstruction image without attenuation correction is used At the same time, an approximate linear attenuation coefficient image conjecture is selected The approximate attenuation correction image obtained by performing attenuation correction

[0103] Here, the image without attenuation correction Although obvious attenuation artifacts exist, the structural information of different tissues is still retained. For example, although the patient's edge is highlighted, the edge range of the patient can still be determined; although the contrast of the lung uptake is incorrect, the lung contour can still be outlined. Approximately attenuation-corrected image Since the linear attenuation image used for attenuation correction is an approximate result, attenuation artifacts are still inevitable. For example, the lung contour is unclear, but the segmentation of the liver organ is relatively more accurate. Therefore, the un-attenuation-corrected PET image and the approximately attenuation-corrected image are used as the dual-channel mapping input, and two PET prior images are used in combination and interactively verified to achieve the purpose of more accurate estimation of the linear attenuation image, that is

[0104]

[0105] Without loss of generality, the mapping input can also only select the un-attenuated PET image or the approximately attenuation-corrected image or select to use the weighted sum of the un-attenuated PET image and the approximately attenuation-corrected image as the network input, and select according to actual needs.

[0106] It should be noted that since PET scans are always used in combination with other modality imaging, the approximate linear attenuation coefficient distribution can be based on other modality images. Taking the PET / CT imaging system as an example, the high signal-to-noise ratio image obtained by the CT system can be used to convert the CT values into a photon linear attenuation coefficient distribution image at 511 KeV energy through the bilinear method; taking the PET / MR imaging system as an example, the MR image is segmented for different regions (such as soft tissue, fat, lung, air, etc.), and then the corresponding theoretical linear attenuation coefficient values are directly assigned (for example, select the soft tissue region and assign a value of 0.0975 cm -1 、the fat region is assigned a value of 0.0864 cm -1 、the lung region is assigned a value of 0.0224 cm -1 、the air region is assigned a value of 0). During the calculation process of the linear attenuation coefficient distribution it is possible to choose to interpolate the initial distribution image to reduce the partial volume effect.

[0107] Step 05: Based on formulas (3) and (4), the solution of the radioactivity distribution image x and the linear attenuation coefficient image μ becomes a constrained maximum likelihood function optimization problem, that is:

[0108]

[0109] In this embodiment, the augmented Lagrangian formula can be used to solve this constrained optimization problem, and formula (5) is written as a log-likelihood function with constraint terms:

[0110]

[0111] where ρ is a hyperparameter and a fixed value, used to adjust the weight between the log-likelihood function and the learning network penalty term, usually selected before training. Δμ is the change step of the linear attenuation coefficient image μ, which is an intermediate variable and represents the change amount of μ. This change amount of μ comes from formula (2) because when constructing the log-likelihood function, a separate constraint on Δμ (i.e., the L2-Norm of Δμ) is required to ensure that the change amplitude of μ is not too large.

[0112] Step 06: The log-likelihood function L with constraint terms in formula (6) ρ is a very complex function for the unknowns x and μ, and an iterative algorithm needs to be used to gradually approximate the optimal solution. For the unknown PET radioactivity distribution x, keeping the linear attenuation coefficient distribution μ and the learning network parameters θ as constants, maximize the log-likelihood function L of the constraint terms ρ , and obtain the iteratively updated radioactivity distribution:

[0113]

[0114] In the formula, n represents the current iteration number. The initial iteration value of the PET radioactivity distribution x can be selected as a full-space normal constant distribution. Since the PET image represents the radioactivity distribution and its value cannot be negative, the total initial value in this embodiment can be set as the pixel value of the full space, such as 1000.

[0115] In this embodiment, for the solution of the PET radioactivity distribution x, commonly used algorithms in the industry such as the Maximum Likelihood Expectation Maximization (MLEM), its accelerated algorithm Ordered Subset Expectation Maximization (OSEM), or the Maximum a Posteriori (MAP) algorithm, etc. can be selected. This embodiment does not limit it, and can be selected according to actual needs.

[0116] It is understandable that during the implementation process, first, the linear attenuation coefficient distribution μ and the training network parameters θ are kept constant, and the logarithmic likelihood function is maximized to solve for the PET radioactivity distribution x. Then, the PET activity distribution x is kept constant, and the logarithmic likelihood function with a constraint term is maximized to alternately solve for the linear attenuation coefficient distribution μ and the training deep learning network parameters θ. By operating alternately in this way, the attenuation correction is continuously corrected to approximate the true attenuation situation, and finally, the estimated values of x and μ that meet the requirements of the maximized objective function are obtained.

[0117] Step 07: For the solution equation of the above formula (6), this embodiment provides a specific calculation and solution process.

[0118] For formula (6), keeping the PET radioactivity distribution x constant, the logarithmic likelihood function L with a constraint term is maximized for the unknown attenuation coefficient distribution μ and the learning network parameters θ ρ , and it is solved using the alternating direction method of multipliers (ADMM) iterative algorithm. The process is divided into the following three steps:

[0119]

[0120]

[0121]

[0122] In the formula, n represents the current iteration number. After using the ADMM algorithm, the constrained optimization problem is decoupled into a network training sub-problem (8) with the L2 norm as the loss function and a solution sub-problem (9) of the attenuation coefficient distribution μ with a penalty term.

[0123] In each step of the iteration, only one variable is updated while the other two variables are fixed, and this is repeated alternately for updating.

[0124] Specifically: First, keep the linear attenuation coefficient distribution μ and the step size increment Δμ unchanged, and update the network parameters θ by training the learning network, as shown in formula (8); then keep the network parameters θ and the linear attenuation coefficient step size increment Δμ unchanged, and iteratively update the linear attenuation coefficient distribution μ, as shown in formula (9); finally, keep the linear attenuation coefficient distribution μ and the network parameters θ unchanged, and update the linear attenuation coefficient step size increment Δμ, as shown in formula (10). In this way, the three variables iteratively approach the optimal solution to obtain an accurate estimate of the linear attenuation coefficient distribution.

[0125] To accelerate the convergence speed, the pre-trained network can be used to generate general network parameters as the initial values for network parameter iteration, and then fine-tuning can be performed for specific scanned patients. The initial value of the iteration of the attenuation coefficient distribution μ can be all 0, or

[0126] The mapping network in this embodiment can be a CNN network, a Unet network, a GAN network, or other networks. Without loss of generality, the loss function can also be an L1 norm, KL divergence, etc., or multiple loss functions can be weighted and summed, and it can be selected according to actual needs. The loss function here can be the loss function used in the process of training the network.

[0127] The above pre-training refers to using a large amount of training data to train the model to complete the mapping from the prior PET image to the linear attenuation coefficient image. In this embodiment, for the actually scanned patients, the network parameters need to be fine-tuned to better adapt to the actual situation, and the pre-trained network parameters can be used as the starting values in the process of network fine-tuning, which ensures the network convergence speed.

[0128] Step 08: Affected by different sites, different devices, and different scanning parameters, there are great differences in the quality of PET images. Therefore, in this embodiment, it is necessary to pre-train a general learning network / mapping network as the initial value for training the current network parameters, and then fine-tune the training parameters according to the actual PET acquisition data. This can not only ensure that the results of the linear attenuation coefficient are consistent with the actual acquisition data, but also greatly reduce the requirements for data generalization in training the network.

[0129] Specifically, in order to be able to fully extract the features of the PET image, a pre-constructed deep learning network G is selected to implement the mapping from the PET image to the linear attenuation coefficient image.

[0130] For example, when training the deep learning network G, taking PET / CT as an example, the PET images in the training samples can include unattenuated PET images and approximately attenuation-corrected PET images Taking these two PET images as dual-channel inputs, the linear attenuation coefficient image μ generated by mapping the PET image DL is used as the output, and is compared with the true linear attenuation image μ obtained by CT scanning CT By optimizing the training network parameters θ to minimize the loss function Φ, finally, the PET image can be translated into an accurate linear attenuation coefficient image, that is:

[0131]

[0132] The superscript represents the solution result of this value.

[0133] The training samples in the training data can come from simulation or actual acquisition. All PET images in the training data need to be preprocessed. Through the preprocessing screening, it is ensured that the linear attenuation coefficient image and the PET image in each sample match, and there are no truncation or motion artifacts. That is to say, in the training, the data input to G is the PET reconstruction image, the output is the linear attenuation coefficient image mapped from the PET image, and the learning target is the linear attenuation coefficient image obtained from the actually acquired CT image. The network training is to optimize the network parameters to ensure that the network output is similar to the actual result.

[0134] It can be understood that the deep learning network G can be a CNN network, a Unet network, a GAN network or other networks. Usually, the input of the deep learning network can only select the unattenuated PET image or the approximately attenuation-corrected image or select to sum the unattenuated PET image and the approximately attenuation-corrected image as the network input. The above loss function Φ can be used to scale the similarity between μ DL and μ CT . The L1 norm, L2 norm, KL divergence, etc. can be selected, or multiple loss functions can be weighted and summed.

[0135] For example, in the case of Figure 2 (a) to Figure 2 (d) as shown, Figure 2 (a) is a schematic diagram of the PET image without attenuation correction, Figure 2 (b) is a schematic diagram of the approximately attenuation-corrected PET image, Figure 2 (c) is a schematic diagram of the PET image with attenuation correction using the method of the present invention, Figure 2 (d) is the estimation result of the prior distribution of the linear attenuation coefficient obtained by using the learning network. It can be seen that Figure 2 the result of (c) is better than the first two PET images, with a fast convergence speed, high reliability, and no artifacts.

[0136] The method of this embodiment does not have the problem of attenuation image truncation, which is convenient for doctors to scan large-weight patients; the attenuation correction iteration process is adjusted by the prior estimation of the linear attenuation coefficient generated by the deep learning network, and both the quantitative property and the tissue distribution are more accurate than the original iterative algorithm, so the stability and convergence speed of the attenuation correction algorithm are greatly improved; the linear attenuation coefficient generated by the deep learning network is applied to the attenuation coefficient iterative algorithm, which solves the problem of generalization of PET acquisition data, simplifies the construction difficulty of the learning network, and increases the stability of the network; PET acquisition does not depend on other modalities and can be applied in a single PET scan, reducing the requirements for the scanning environment and expanding the application scenarios.

[0137] In addition, an embodiment of the present invention further provides a PET system, which includes: a memory and a processor; computer program instructions are stored in the memory, and the processor executes the computer program instructions stored in the memory, specifically implementing the above method for obtaining the radioactive activity distribution of a PET, etc.

[0138] It should be noted that in the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word "comprising" does not exclude the presence of elements or steps not listed in a claim. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The present invention can be implemented by means of hardware including several different elements and by means of a suitably programmed computer. In a claim listing several means, several of these means can be embodied by one and the same piece of hardware. The use of the terms first, second, third, etc. is for convenience of expression only and does not denote any order. These terms can be understood as part of the name of the element.

[0139] In addition, it should be noted that in the description of this specification, the descriptions of the terms "one embodiment", "some embodiments", "embodiment", "example", "specific example" or "some examples", etc. mean that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic descriptions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0140] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications after learning the basic creative concepts. Therefore, the claims should be construed to include the preferred embodiments as well as all changes and modifications falling within the scope of the present invention.

[0141] Obviously, those skilled in the art can make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention should also include these modifications and variations.

Claims

1. A method for obtaining the radioactive activity distribution of PET, characterized in that, Including: S10. For the detection data used for medical image reconstruction, obtain a first PET image without attenuation correction and a second PET image with approximate attenuation correction of the detection data. The second PET image is an image reconstructed after attenuating and correcting the first PET image based on the empirical value of the linear attenuation correction coefficient in a specified region; S20. According to the pre-constructed mapping from the PET prior image α to the linear attenuation coefficient image μ, and the known log-likelihood function with unknowns being the PET radioactivity distribution x and the linear attenuation coefficient distribution μ, obtain a log-likelihood function with a constraint term, where the constraint term is the mapping from the PET prior image α to the linear attenuation coefficient image μ; The PET prior image α is the first PET image without attenuation correction and / or the second PET image with approximate attenuation correction; the unknowns in the log-likelihood function with the constraint term are: x, μ, and the parameters of the mapping; S30. According to the log-likelihood function with the constraint term, use an iterative algorithm to maximize the log-likelihood function of the constraint term. When the end condition is reached, obtain an estimated value of the PET radioactivity distribution x; The initial values of x, μ, and the parameters of the mapping in the iterative algorithm for maximizing the log-likelihood function of the constraint term are specified values; Before S20, construct a mapping from the PET prior image α to the linear attenuation coefficient image μ; The mapping includes: Formula (1) f represents the mapping of the trained model, representing the parameters of the mapping, and α represents the input of the trained model; S20 includes: For a known logarithmic likelihood function L and , the logarithmic likelihood function with constraint terms is obtained as follows: ; Formula (2) where ρ is a hyperparameter used to adjust the weight between the log-likelihood function and the learning network penalty term, Δμ is the change step of the linear attenuation coefficient image μ, x represents the PET radioactivity distribution, and y represents the detection data.

2. The method according to claim 1, characterized in that: For formula (2), an alternating strategy is adopted based on a known solution algorithm to maximize the log-likelihood function \(L\) with constraint terms ρ , and an estimated value of \(x\) that satisfies the requirement of maximizing the log-likelihood function \(L\) with constraint terms ρ is obtained as the output value; where the alternating iteration strategy includes: in each step of the iteration, only update one variable while fixing the other two variables, and repeat the update alternately in this way; Specifically, the mapping parameter θ is the initial value for accelerating the convergence rate pre-trained by a CNN network, Unet network, or GAN network as a training model; The initial value of the attenuation coefficient distribution μ is 0 or a second image of approximate attenuation correction ; The initial value of the PET radioactivity distribution x is a set value; The known solution algorithm is the maximum likelihood expectation maximization algorithm MLEM, the ordered subset expectation maximization algorithm OSEM, or the maximum a posteriori estimation algorithm MAP.

3. The method according to claim 1, characterized in that: For Equation (2), keeping the PET radioactivity distribution x as a constant, maximize the log-likelihood function L with constraint terms with respect to the unknown attenuation coefficient distribution μ and the mapping parameter θ ρ , and solve it using the alternating direction method of multipliers (ADMM) iterative algorithm. The process is divided into the following three steps: （8）； （9）； （10）； where n represents the current iteration number, and n iterations satisfy the end condition; when using the ADMM algorithm, decouple the constrained optimization problem into a network training sub-problem with the L2 norm as the loss function - corresponding to formula (8) and a sub-problem for solving μ with a penalty term - corresponding to formula (9); Specifically, first keep the linear attenuation coefficient distribution μ and the step size increase Δμ unchanged, and update θ based on formula (8); then based on formula (9), keep θ and Δμ unchanged, and iteratively update μ; based on formula (10), keep μ and θ unchanged, and update Δμ, and iterate in this way to approximate the optimal solution.

4. The method according to claim 2, characterized in that: When the medical image is a PET image, before S10, the method further includes: S00. Obtain training samples for training a model based on the reconstructed medical image and the matched associated image; Wherein, each training sample includes: the reconstructed PET image / simulated PET image, the approximate linear attenuation correction coefficient corresponding to the PET image, and other modality images corresponding to the PET image, where the other modality images are used to obtain the true linear attenuation correction coefficient, and the true linear attenuation correction coefficient is used to verify whether the trained model converges; S01. Train the model based on the training samples to obtain a trained model; In the trained model, the mapping parameter θ minimizes the value of the loss function Φ for optimizing the trained model.

5. The method according to claim 4, wherein Training the model based on the training samples includes: Input the approximate linear attenuation correction coefficient of each training sample into the model to obtain an output, and compare the output with the true linear attenuation correction coefficient obtained from the other modality images in the training sample by means of the loss function Φ; and / or, Input the reconstructed attenuation-free PET image of each training sample into the model to obtain an output, and compare the output with the true linear attenuation correction coefficient obtained from the other modality images in the training sample by means of the loss function Φ; and / or, Sum the reconstructed attenuation-free PET image and the approximate linear attenuation correction coefficient of each training sample, input the summed image into the model to obtain an output, and compare the output with the true linear attenuation correction coefficient obtained from the other modality images in the training sample by means of the loss function Φ; The loss function Φ is one or more of the L1 norm, L2 norm, and KL divergence, and is used to scale the similarity between each output of the model in training and the true linear attenuation correction coefficient to which the output belongs.

6. A PET system, characterized in that, It includes: A memory and a processor; computer program instructions are stored in the memory, and the processor executes the computer program instructions stored in the memory to specifically execute a method for obtaining the PET radioactivity distribution according to any one of claims 1 to 5 above.

7. A computer-readable storage medium, characterized in that, A computer program is stored on the computer-readable storage medium, and when the computer program is run by the processor, it executes a method for obtaining the PET radioactivity distribution according to any one of claims 1 to 5 above.

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