CN109741411B - Low-dose PET image reconstruction method, device, equipment and medium based on gradient domain - Google Patents

Abstract

The invention is applicable to the technical field of medical PET imaging, and provides a low-dose PET image reconstruction method, a device, equipment and a medium based on a gradient domain, wherein the method comprises the following steps: according to projection data acquired by PET equipment and a system matrix of the PET equipment, carrying out image reconstruction on a pre-initialized PET image to be reconstructed through a PET image reconstruction algorithm to obtain an initial reconstructed PET image, carrying out joint optimization solution on a pre-constructed image reconstruction equation and a pre-constructed gradient domain image feature selection equation according to the initial reconstructed PET image by adopting Lagrange multiplication to obtain a target reconstructed PET image corresponding to the initial reconstructed PET image, thereby improving the reconstruction speed of the low-dose PET image, reducing the artifact degree of the reconstructed image and further improving the image quality of the low-dose PET image reconstruction.

Description

Method, device, equipment and medium for low-dose PET image reconstruction based on gradient domain

technical field

The invention belongs to the technical field of medical PET imaging, and in particular relates to a gradient-domain-based low-dose PET image reconstruction method, device, equipment and medium.

Background technique

Positron Emission Tomography (PET for short) is an emission imaging technique (Emission Tomography, ET for short), which displays the metabolism of different tissues by injecting radiopharmaceuticals into the body. PET technology is a new type of imaging technology applied clinically after Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). It has shown excellent performance in the fields of disease research and new drug development research.

In PET imaging, radiopharmaceuticals are actually molecular carriers that attach to specific physiological tissues or pathological processes. Radioactive substances are purposefully distributed in the human body under the leadership of drugs. The purpose of PET imaging is actually to obtain the distribution map of radioactive substances in the human body. Its working principle is: to mark some radioactive nuclear elements, such as O-15, C-11, N-13 and F-18, etc. in the human body. The desired compound is then injected into the subject's body through intravenous injection in the arm. When the labeled compound participates in the metabolism of the body, the radioactive nuclear element decays and releases a positron (an electron with a positive charge), which annihilates with its surrounding (negatively charged) electrons to produce two Gamma atoms with an energy of 511keV. Ma Photon. The pair of photons shoot out in opposite directions on a straight line, and the gamma camera outside the body can detect all the photons emitted in a specific area, and then design a certain algorithm to approximate the distribution of radioactive substances in the human body.

Because the radiopharmaceuticals used in PET examinations will produce radiation to those who are in close contact with the medicines, and the chances of people who are exposed to the radiation will be much higher than normal people, and the consumption of radiopharmaceuticals occupies a certain part of the cost of PET examinations. proportion. Therefore, according to the principle of As Low As Reasonably Achievable (ALARA) proposed by the International Commission on Radiological Protection (ICRP), in the clinical diagnosis of PET, it is hoped that the minimum dose can be used to obtain images that meet clinical needs. , to minimize the radiation dose to the patient.

However, when performing PET image reconstruction on the measurement data obtained by low-dose sampling, the existing traditional PET image reconstruction algorithm reconstructs the image slowly, which in turn causes motion artifacts in the reconstructed image, which will directly affect the doctor's diagnosis Behavior.

Contents of the invention

The purpose of the present invention is to provide a low-dose PET image reconstruction method, device, equipment and medium based on the gradient domain, aiming to solve the problem of low-dose PET image reconstruction due to the inability of the prior art to provide an effective low-dose PET image reconstruction method. The reconstruction speed is slow and the reconstruction image quality is poor.

On the one hand, the present invention provides a kind of low-dose PET image reconstruction method based on gradient field, and described method comprises the following steps:

When a reconstruction request of a low-dose PET image is received, the projection data collected by the PET device is obtained, and the system matrix of the PET device is obtained;

performing image reconstruction on a pre-initialized PET image to be reconstructed through a preset PET image reconstruction algorithm according to the projection data and the system matrix, to obtain an initial reconstructed PET image;

According to the initial reconstructed PET image, Lagrangian multiplication is used to jointly optimize and solve the pre-built image reconstruction equation and the pre-built gradient domain image feature selection equation to obtain the target reconstructed PET image corresponding to the initial reconstructed PET image.

In another aspect, the present invention provides a gradient domain-based low-dose PET image reconstruction device, the device comprising:

A parameter acquisition unit, configured to acquire the projection data collected by the PET device and obtain the system matrix of the PET device when a reconstruction request of the low-dose PET image is received;

An initial reconstruction unit, configured to perform image reconstruction on a pre-initialized PET image to be reconstructed through a preset PET image reconstruction algorithm according to the projection data and the system matrix, to obtain an initial reconstructed PET image; and

The reconstructed image obtaining unit is used to jointly optimize and solve the pre-built image reconstruction equation and the pre-built gradient domain image feature selection equation according to the initial reconstructed PET image by using Lagrangian multiplication to obtain the initial reconstructed PET image Corresponding target reconstructed PET images.

On the other hand, the present invention also provides a computing device, including a memory, a processor, and a computer program stored in the memory and operable on the processor, when the processor executes the computer program, the Steps as described above for gradient-domain-based low-dose PET image reconstruction method.

On the other hand, the present invention also provides a computer-readable storage medium, the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the above-mentioned low-dose PET image reconstruction based on the gradient domain is realized. steps described in the method.

According to the projection data collected by the PET equipment and the system matrix of the PET equipment, the present invention reconstructs the pre-initialized PET image to be reconstructed through the PET image reconstruction algorithm to obtain the initial reconstructed PET image. According to the initial reconstructed PET image, the Lager Langer multiplication jointly optimizes the pre-built image reconstruction equation and the pre-built gradient domain image feature selection equation to obtain the target reconstructed PET image corresponding to the initial reconstructed PET image, thereby improving the reconstruction speed of low-dose PET images and reducing The degree of artifacts in the reconstructed images, thereby improving the image quality of low-dose PET image reconstruction.

Description of drawings

Fig. 1 is a flow chart of the realization of the low-dose PET image reconstruction method based on the gradient domain provided by Embodiment 1 of the present invention;

Fig. 2 is the realization flow chart that adopts Bregman iterative method to iteratively solve Lagrangian equation in embodiment one of the present invention;

Fig. 3 is a schematic structural diagram of a low-dose PET image reconstruction device based on a gradient domain provided by Embodiment 2 of the present invention;

Fig. 4 is a schematic diagram of an optimal structure of a low-dose PET image reconstruction device based on a gradient domain provided by Embodiment 2 of the present invention;

Fig. 5 is a schematic diagram of another preferred structure of the gradient domain-based low-dose PET image reconstruction device provided by Embodiment 2 of the present invention; and

FIG. 6 is a schematic structural diagram of a computing device provided by Embodiment 3 of the present invention.

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

The specific realization of the present invention is described in detail below in conjunction with specific embodiment:

Embodiment one:

Figure 1 shows the implementation process of the gradient domain-based low-dose PET image reconstruction method provided by Embodiment 1 of the present invention. For the convenience of illustration, only the parts related to the embodiment of the present invention are shown, and the details are as follows:

In step S101, when a reconstruction request of a low-dose PET image is received, the projection data collected by the PET device is obtained, and the system matrix of the PET device is obtained.

Embodiments of the present invention are applicable to medical image processing platforms, systems or devices, such as personal computers, servers, and the like. When a request for reconstruction of a low-dose PET image is received, the under-sampled projection data collected by the PET device under low-dose conditions is obtained, and the system matrix of the PET device is obtained, which is based on the geometric structure information of the PET device calculated.

In step S102, according to the projection data and the system matrix, the pre-initialized PET image to be reconstructed is reconstructed through a preset PET image reconstruction algorithm to obtain an initial reconstructed PET image.

In the embodiment of the present invention, according to the projection data and the system matrix, the pre-initialized PET image to be reconstructed is iteratively operated for a preset number of times through the preset PET image reconstruction algorithm, so as to perform image reconstruction on the PET image to be reconstructed, and obtain the initial reconstruction PET image, wherein the PET image to be reconstructed is a two-dimensional image, and the preset PET image reconstruction algorithm is Maximum Likelihood Expectation Maximized (MLEM for short) or Ordered Subset Expectation Maximization algorithm (Ordered Subset Expectation Maximization) , referred to as OSEM) or Maximum A Posterior probability algorithm (Maximum A Posterior, MAP).

When initializing the PET image to be reconstructed, as an example, all pixel values of the PET image to be reconstructed are initialized to zero.

In step S103, according to the initial reconstructed PET image, the pre-constructed image reconstruction equation and the pre-constructed gradient domain image feature selection equation are jointly optimized and solved by Lagrangian multiplication, and the target reconstructed PET image corresponding to the initial reconstructed PET image is obtained .

进行联立，得到对应的拉格朗日方程

再对该拉格朗日方程进行优化求解，最终得到初始重建PET图像对应的目标重建PET图像，其中，y_u为投影数据，G_u为系统矩阵，m为待重建PET图像(也即目标重建PET图像)，v₁为预设的权重参数，R_l为图像块提取矩阵，即根据该R_l从梯度图像ω中提取l个图像块，D为梯度图像ω的特征矩阵，α_l为从梯度图像ω中提取出的第l个图像块对应的特征向量，ω⁽ⁱ⁾表示初始重建PET图像对应的水平/垂直梯度图像，i∈{1,2}表示所述梯度图像ω的方向(水平/垂直)，L表示对特征向量的稀疏度的控制系数。In the embodiment of the present invention, the pre-built image reconstruction equation y _u =G _u m and the pre-built gradient domain image feature selection equation are combined by Lagrangian multiplication

Simultaneously, get the corresponding Lagrangian equation

Then optimize and solve the Lagrangian equation, and finally obtain the target reconstructed PET image corresponding to the initial reconstructed PET image, where y _u is the projection data, G _u is the system matrix, and m is the PET image to be reconstructed (that is, the target reconstruction PET image), v ₁ is the preset weight parameter, R _l is the image block extraction matrix, that is, extract l image blocks from the gradient image ω according to the R _l , D is the feature matrix of the gradient image ω, and α _l is from The feature vector corresponding to the lth image block extracted from the gradient image ω, ω ⁽ⁱ⁾ represents the horizontal/vertical gradient image corresponding to the initial reconstructed PET image, and i∈{1,2} represents the direction of the gradient image ω ( Horizontal/vertical), L represents the control coefficient for the sparsity of the feature vector.

In the embodiment of the present invention, preferably, the control coefficient L of the feature vector sparsity is set to 5, so as to better reduce the noise of the PET image sparsely represented by the learned feature matrix and feature vector.

When Lagrange multiplication is used to jointly optimize and solve the pre-built image reconstruction equation and the pre-built gradient domain image feature selection equation, preferably, the Bregman iterative method is used to combine the image reconstruction equation and the gradient domain image feature selection equation. Iteratively solves the established Lagrangian equation, thus improving the reconstruction speed of PET images.

Further preferably, the Lagrangian equation is decomposed into a gradient image update function, an iterative error correction function, a PET image reconstruction function, and a feature extraction function using the Bregman iterative method, so that the gradient image update function, the iterative error correction function, and the PET image The reconstruction function and the feature extraction function are iteratively solved to obtain the target reconstructed PET image corresponding to the initial reconstructed PET image, thereby further improving the reconstruction speed of the PET image and improving the image quality of the reconstructed target reconstructed PET image.

获得的特征矩阵D和特征向量α_l用来作为下一轮迭代中对梯度图像ω进行更新的初始值，从而将初始重建PET图像从图像域转换到梯度域，对梯度域图像进行特征学习，以通过学习到的特征矩阵和特征向量稀疏表示初始重建PET图像，从而降低初始重建PET图像中的噪声，进而提高后续PET图像的重建效果。其中，k为当前迭代次数。Preferably, the feature extraction function obtained by decomposing the Lagrangian equation is

The obtained feature matrix D and feature vector α _l are used as the initial value for updating the gradient image ω in the next iteration, so as to convert the initial reconstructed PET image from the image domain to the gradient domain, and perform feature learning on the gradient domain image. The initial reconstructed PET image is sparsely represented by the learned feature matrix and feature vector, so as to reduce the noise in the initial reconstructed PET image, and then improve the reconstruction effect of the subsequent PET image. Among them, k is the current iteration number.

获得的梯度图像ω用来作为下一轮迭代中对目标重建PET图像m进行重建的初始值，从而降低后续重建的目标重建PET图像的伪影程度。其中，v₂为预设的用来在Bregman迭代中控制迭代误差的权重，b为Bregman迭代的误差校正值。Preferably, the gradient image update function obtained by decomposing the Lagrangian equation is

The obtained gradient image ω is used as the initial value for reconstructing the target reconstructed PET image m in the next iteration, thereby reducing the degree of artifacts of the target reconstructed PET image for subsequent reconstruction. Among them, v ₂ is the preset weight used to control the iteration error in the Bregman iteration, and b is the error correction value of the Bregman iteration.

In the embodiment of the present invention, further preferably, v ₂ is set to 1, so as to further reduce the degree of artifacts of the subsequent reconstructed target reconstructed PET image.

获得的误差校正值b用来作为下一轮迭代中对目标重建PET图像m进行重建的初始值，从而提高重建得到的PET图像的图像质量。Preferably, the iterative error correction function obtained by decomposing the Lagrangian equation

The obtained error correction value b is used as an initial value for reconstructing the target reconstructed PET image m in the next iteration, so as to improve the image quality of the reconstructed PET image.

ω^k为第k次迭代的梯度图像，b^k为第k次迭代的误差校正值，从而提高重建得到的PET图像的图像质量。Preferably, the PET image reconstruction function obtained by decomposing the Lagrangian equation

ω ^k is the gradient image of the k-th iteration, and b ^k is the error correction value of the k-th iteration, so as to improve the image quality of the reconstructed PET image.

As shown in Figure 2, preferably, the Bregman iterative method is used to iteratively solve the Lagrangian equation through the following steps:

In step S201, according to the preset initial feature matrix and the preset initial feature vector, a gradient image update function is used to update the gradient image corresponding to the initially reconstructed PET image.

In step S202, according to the updated gradient image and the error correction value obtained by the iterative error correction function, the PET image reconstruction function is used to restore the gradient image from the gradient domain to the image domain to obtain the target reconstructed PET image.

In step S203, it is judged whether the current number of iterations reaches a preset iteration threshold.

In the embodiment of the present invention, when the current number of iterations reaches a preset iteration threshold (for example, 50 times), step S204 is executed; otherwise, step S205 is skipped.

In step S204, the reconstructed PET image of the target is output.

In step S205, set the target reconstructed PET image as the initial reconstructed PET image, and extract a corresponding number of image blocks from the gradient image corresponding to the initial reconstructed PET image according to the preset image block extraction matrix, the gradient image includes the horizontal gradient image and a vertical gradient image.

In the embodiment of the present invention, firstly, the initial reconstructed PET image is converted from the image domain to the gradient domain to obtain the horizontal gradient image and the vertical gradient image. A corresponding number of horizontal image blocks and vertical image blocks.

In step S206, feature learning is performed on the image block until the feature matrix corresponding to the learned gradient image and the feature vector corresponding to the image block satisfy the feature extraction function.

In the embodiment of the present invention, feature learning is performed on the extracted horizontal image block and vertical image block, until the horizontal/vertical feature matrix corresponding to the learned horizontal/vertical gradient image and the horizontal/vertical feature matrix corresponding to the horizontal/vertical image block The vector satisfies the feature extraction function, where each column of the feature matrix is in one-to-one correspondence with the feature vector corresponding to each image block.

In step S207, set the eigenmatrix and eigenvector as the initial eigenmatrix and initial eigenvector respectively, increase the current iteration number by 1, and jump to step S201 to continue the next iteration to reconstruct the PET image.

Through the above step S201-step S207, the Lagrangian equation is iteratively solved to obtain the target reconstructed PET image corresponding to the initial reconstructed PET image, thereby reducing the artifact degree of the reconstructed image and improving the image quality of low-dose PET image reconstruction .

In the embodiment of the present invention, according to the projection data collected by the PET device and the system matrix of the PET device, the pre-initialized PET image to be reconstructed is reconstructed through the PET image reconstruction algorithm to obtain the initial reconstructed PET image, and according to the initial reconstructed PET image image, using Lagrangian multiplication to jointly optimize and solve the pre-built image reconstruction equation and the pre-built gradient domain image feature selection equation, and obtain the target reconstructed PET image corresponding to the initial reconstructed PET image, thereby improving the accuracy of low-dose PET images. The reconstruction speed is improved, and the artifact degree of the reconstructed image is reduced, thereby improving the image quality of low-dose PET image reconstruction.

Embodiment two:

Fig. 3 shows the structure of the gradient domain-based low-dose PET image reconstruction device provided by Embodiment 2 of the present invention. For the convenience of illustration, only the parts related to the embodiment of the present invention are shown, including:

The parameter acquisition unit 31 is configured to acquire the projection data collected by the PET equipment and acquire the system matrix of the PET equipment when a reconstruction request of the low-dose PET image is received;

The initial reconstruction unit 32 is configured to perform image reconstruction on the pre-initialized PET image to be reconstructed through a preset PET image reconstruction algorithm according to the projection data and the system matrix, to obtain an initial reconstructed PET image; and

The reconstructed image obtaining unit 33 is used to jointly optimize and solve the pre-built image reconstruction equation and the pre-built gradient domain image feature selection equation according to the initial reconstructed PET image by using Lagrangian multiplication to obtain the target corresponding to the initial reconstructed PET image Reconstructed PET images.

As shown in Figure 4, preferably, the reconstructed image obtaining unit 33 includes:

The iterative solving unit 331 is used to iteratively solve the Lagrangian equation which is the simultaneous combination of the image reconstruction equation and the gradient domain image feature selection equation by using the Bregman iterative method.

Further preferably, the iterative solving unit 331 includes:

The equation decomposition unit 3311 is used to decompose the Lagrangian equation into gradient image update function, iterative error correction function, PET image reconstruction function, and feature extraction function by adopting Bregman iterative method, so as to update the gradient image function, iterative error correction function , the PET image reconstruction function, and the feature extraction function are iteratively solved to obtain the target reconstructed PET image corresponding to the initial reconstructed PET image.

Further preferably, as shown in Figure 5, the equation decomposition unit 3311 includes:

The gradient image update unit 51 is used to update the gradient image corresponding to the initially reconstructed PET image using the gradient image update function according to the preset initial feature matrix and the preset initial feature vector;

The PET image reconstruction unit 52 is used to restore the gradient image from the gradient domain to the image domain using the PET image reconstruction function according to the updated gradient image and the error correction value obtained by the iterative error correction function, so as to obtain the target reconstructed PET image;

The number of iterations judging unit 53 is used to judge whether the current number of iterations reaches a preset iteration threshold;

The PET image output unit 54 is used to output the reconstructed PET image of the target;

The image block extraction unit 55 is configured to otherwise set the target reconstructed PET image as the initial reconstructed PET image, and extract a corresponding number of image blocks from the gradient image corresponding to the initial reconstructed PET image according to the preset image block extraction matrix, the gradient The image includes a horizontal gradient image and a vertical gradient image;

The feature learning unit 56 is used to perform feature learning on the image block until the feature matrix corresponding to the learned gradient image and the feature vector corresponding to the image block satisfy the feature extraction function; and

The parameter setting unit 57 is used to set the feature matrix and the feature vector as the initial feature matrix and the initial feature vector respectively, and trigger the gradient image update unit 51 to continue the next round of iterations to reconstruct the PET image.

In the embodiment of the present invention, each unit of the low-dose PET image reconstruction device based on the gradient domain can be realized by corresponding hardware or software units, each unit can be an independent software and hardware unit, or can be integrated into a software and hardware unit, It is not intended to limit the present invention. Specifically, for the implementation manner of each unit, reference may be made to the description of the first embodiment above, and details are not repeated here.

Embodiment three:

FIG. 6 shows the structure of a computing device provided by Embodiment 3 of the present invention. For ease of description, only parts related to the embodiment of the present invention are shown.

The computing device 6 of the embodiment of the present invention includes a processor 60 , a memory 61 and a computer program 62 stored in the memory 61 and operable on the processor 60 . When the processor 60 executes the computer program 62 , the steps in the embodiment of the gradient domain-based low-dose PET image reconstruction method described above are implemented, such as steps S101 to S103 shown in FIG. 1 . Alternatively, when the processor 60 executes the computer program 62, the functions of the units in the above-mentioned device embodiments are implemented, for example, the functions of the units 31 to 33 shown in FIG. 3 .

In the embodiment of the present invention, according to the projection data collected by the PET device and the system matrix of the PET device, the pre-initialized PET image to be reconstructed is reconstructed through the PET image reconstruction algorithm to obtain the initial reconstructed PET image, and according to the initial reconstructed PET image image, using Lagrangian multiplication to jointly optimize and solve the pre-built image reconstruction equation and the pre-built gradient domain image feature selection equation, and obtain the target reconstructed PET image corresponding to the initial reconstructed PET image, thereby improving the accuracy of low-dose PET images. The reconstruction speed is improved, and the artifact degree of the reconstructed image is reduced, thereby improving the image quality of low-dose PET image reconstruction.

The computing device in the embodiment of the present invention may be a personal computer or a server. For the steps to be implemented when the processor 60 in the computing device 6 executes the computer program 62 to implement the gradient domain-based low-dose PET image reconstruction method, reference may be made to the description of the foregoing method embodiments, and details are not repeated here.

Embodiment four:

In an embodiment of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the above-mentioned embodiment of the gradient-domain-based low-dose PET image reconstruction method is implemented The steps in, for example, steps S101 to S103 shown in FIG. 1 . Alternatively, when the computer program is executed by the processor, the functions of the units in the above-mentioned device embodiments are implemented, for example, the functions of the units 31 to 33 shown in FIG. 3 .

In the embodiment of the present invention, according to the projection data collected by the PET device and the system matrix of the PET device, the pre-initialized PET image to be reconstructed is reconstructed through the PET image reconstruction algorithm to obtain the initial reconstructed PET image, and according to the initial reconstructed PET image image, using Lagrangian multiplication to jointly optimize and solve the pre-built image reconstruction equation and the pre-built gradient domain image feature selection equation, and obtain the target reconstructed PET image corresponding to the initial reconstructed PET image, thereby improving the accuracy of low-dose PET images. The reconstruction speed is improved, and the artifact degree of the reconstructed image is reduced, thereby improving the image quality of low-dose PET image reconstruction.

The computer-readable storage medium in the embodiments of the present invention may include any entity or device or recording medium capable of carrying computer program codes, such as ROM/RAM, magnetic disk, optical disk, flash memory and other memories.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention should be included in the protection of the present invention. within range.

Claims (14)

1. A low-dose PET image reconstruction method based on gradient domain, characterized in that said method comprises the steps of: When a reconstruction request of a low-dose PET image is received, the projection data collected by the PET device is obtained, and the system matrix of the PET device is obtained; performing image reconstruction on a pre-initialized PET image to be reconstructed through a preset PET image reconstruction algorithm according to the projection data and the system matrix, to obtain an initial reconstructed PET image; According to the initial reconstructed PET image, the pre-constructed image reconstruction equation and the pre-constructed gradient domain image feature selection equation are jointly optimized and solved by using Lagrangian multiplication to obtain the target reconstructed PET image corresponding to the initial reconstructed PET image; The method uses Lagrange multiplication to jointly optimize and solve the pre-built image reconstruction equation and the pre-built gradient domain image feature selection equation to obtain the target reconstructed PET image corresponding to the initial reconstructed PET image, which includes: using Lager Langerian multiplication combines the pre-constructed image reconstruction equation and the pre-constructed gradient domain image feature selection equation to obtain a corresponding Lagrangian equation; and, optimizing and solving the Lagrangian equation to obtain a target reconstructed PET image corresponding to the initial reconstructed PET image; The pre-constructed image reconstruction equation includes y _u = G _u m, and the pre-constructed gradient domain image feature selection equation includes The corresponding Lagrangian equation obtained includes: Where y _u is the projection data, G _u is the system matrix, m is the PET image to be reconstructed (that is, the target reconstructed PET image), v ₁ is the preset weight parameter, R ₁ is the image block extraction matrix, that is, according to R ₁₁ from One image block is extracted from the gradient image ω, D is the feature matrix, a ₁ is the feature vector corresponding to the first image block, ω ⁽ⁱ⁾ represents the horizontal/vertical gradient image corresponding to the initial reconstructed PET image, i∈{1, 2} represents the direction horizontal/vertical of the gradient image ω, and L represents the control coefficient for the sparsity of the feature vector. 2. The method according to claim 1, wherein the step of jointly optimizing and solving the pre-built image reconstruction equation and the pre-built gradient domain image feature selection equation using Lagrange multiplication comprises: The Bregman iterative method is used to iteratively solve the Lagrangian equation which is the simultaneous combination of the image reconstruction equation and the gradient domain image feature selection equation. 3. method as claimed in claim 2, is characterized in that, adopts Bregman iterative method to carry out the step of iterative solution to described Lagrangian equation, comprising: The Lagrangian equation is decomposed into a gradient image update function, an iterative error correction function, a PET image reconstruction function, and a feature extraction function using the Bregman iterative method, so as to update the gradient image function, iterative error correction function, and PET image reconstruction function. , and the feature extraction function are iteratively solved to obtain the target reconstructed PET image corresponding to the initial reconstructed PET image. 4. method as claimed in claim 3, is characterized in that, adopts Bregman iterative method to carry out the step of iterative solution to described Lagrangian equation, comprising: Using the gradient image update function to update the gradient image corresponding to the initially reconstructed PET image according to the preset initial feature matrix and the preset initial feature vector; Using the PET image reconstruction function to restore the gradient image from the gradient domain to the image domain according to the updated gradient image and the error correction value obtained by the iterative error correction function to obtain a target reconstructed PET image; Determine whether the current number of iterations reaches the preset iteration threshold; If yes, output the reconstructed PET image of the target; Otherwise, set the target reconstructed PET image as the initial reconstructed PET image, and extract a corresponding number of image blocks from the gradient image corresponding to the initial reconstructed PET image according to a preset image block extraction matrix, the gradient The image includes a horizontal gradient image and a vertical gradient image; Perform feature learning on the image block until the learned feature matrix corresponding to the gradient image and the feature vector corresponding to the image block satisfy the feature extraction function; Setting the feature matrix and the feature vector as the initial feature matrix and the initial feature vector respectively, and jumping to the step of using the gradient image update function to update the gradient image. 5. method as claimed in claim 3, is characterized in that, described feature extraction function is K is the current iteration number. 6. The method according to claim 3, wherein the gradient image update function Among them, V ₂ represents the weight of control iteration error in Bregman iteration, and b is the error correction value of Bregman iteration. 7. The method of claim 3, wherein the iterative error correction function 8. The method according to claim 3, wherein the PET image reconstruction function V ₁ is the preset weight parameter, ω ^k is the gradient image of the k-th iteration, and b ^k is the error correction value of the k-th iteration. 9. A gradient-domain-based low-dose PET image reconstruction device, characterized in that the device comprises: A parameter acquisition unit, configured to acquire the projection data collected by the PET device and obtain the system matrix of the PET device when a reconstruction request of the low-dose PET image is received; An initial reconstruction unit, configured to perform image reconstruction on a pre-initialized PET image to be reconstructed through a preset PET image reconstruction algorithm according to the projection data and the system matrix, to obtain an initial reconstructed PET image; and The reconstructed image obtaining unit is used to jointly optimize and solve the pre-built image reconstruction equation and the pre-built gradient domain image feature selection equation according to the initial reconstructed PET image by using Lagrangian multiplication to obtain the initial reconstructed PET image Corresponding target reconstructed PET images. 10. The device according to claim 9, wherein the reconstructed image obtaining unit comprises: The iterative solving unit is used to iteratively solve the Lagrangian equation which is the simultaneous combination of the image reconstruction equation and the gradient domain image feature selection equation by using the Bregman iterative method. 11. The device according to claim 10, wherein the iterative solving unit comprises: The equation decomposition unit is used to decompose the Lagrangian equation into gradient image update function, iterative error correction function, PET image reconstruction function, and feature extraction function by adopting Bregman iterative method, so that the gradient image update function, iterative error correction Function, PET image reconstruction function, and feature extraction function are iteratively solved to obtain the target reconstructed PET image corresponding to the initial reconstructed PET image. 12. The device according to claim 11, wherein the equation decomposition unit comprises: a gradient image update unit, configured to use the gradient image update according to a preset initial feature matrix and a preset initial feature vector The function updates the gradient image corresponding to the initial reconstructed PET image; The PET image reconstruction unit is configured to use the PET image reconstruction function to restore the gradient image from the gradient domain to the image domain according to the updated gradient image and the error correction value obtained by the iterative error correction function, to obtain Target reconstructed PET image; The number of iterations judging unit is used to judge whether the current number of iterations reaches a preset iteration threshold; A PET image output unit, configured to output the reconstructed PET image of the target; The image block extraction unit is configured to, otherwise, set the target reconstructed PET image as the initial reconstructed PET image, and extract a corresponding amount from the gradient image corresponding to the initial reconstructed PET image according to a preset image block extraction matrix An image block, the gradient image includes a horizontal gradient image and a vertical gradient image; A feature learning unit, configured to perform feature learning on the image block until the learned feature matrix corresponding to the gradient image and the feature vector corresponding to the image block satisfy the feature extraction function; and a parameter setting unit, configured to set the eigenmatrix and the eigenvector as the initial eigenmatrix and the initial eigenvector, respectively, and trigger the gradient image update unit to execute the Gradient image update steps. 13. A computing device, comprising a memory, a processor, and a computer program stored in the memory and operable on the processor, characterized in that, when the processor executes the computer program, the computer program according to claim The step of any one of 1 to 8. 14. A computer-readable storage medium, the computer-readable storage medium storing a computer program, characterized in that, when the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented .

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