WO2020118828A1 - 基于梯度域的低剂量pet图像重建方法、装置、设备及介质 - Google Patents

基于梯度域的低剂量pet图像重建方法、装置、设备及介质 Download PDF

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WO2020118828A1
WO2020118828A1 PCT/CN2019/071098 CN2019071098W WO2020118828A1 WO 2020118828 A1 WO2020118828 A1 WO 2020118828A1 CN 2019071098 W CN2019071098 W CN 2019071098W WO 2020118828 A1 WO2020118828 A1 WO 2020118828A1
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image
gradient
pet
pet image
reconstructed
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胡战利
杨永峰
李快
梁栋
刘新
郑海荣
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Shenzhen Institute of Advanced Technology of CAS
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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—Two-dimensional [2D] image generation
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  • 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.
  • PET Positron emission tomography
  • CT Computer Tomography
  • MRI Magnetic Resonance Imaging
  • the radiopharmaceutical is actually a molecular carrier, which is attached to a specific physiological tissue or pathological process.
  • the radioactive material is purposely distributed in the human body under the leadership of drugs.
  • the purpose of PET imaging is actually to obtain the distribution map of radioactive materials 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 in the human metabolism
  • the desired compound is then injected into the subject through arm vein injection.
  • the radioactive nuclear element decays and releases positrons (electrons with a positive charge).
  • the positrons and their surrounding (negatively charged) electrons annihilate, producing two 511keV gamma Ma photon.
  • the pair of photons are emitted in the opposite direction on a straight line.
  • Using an external gamma camera can detect all photons emitted in a specific area, and then design a certain algorithm to approximate the distribution of radioactive materials in the human body.
  • the purpose of the present invention is to provide a method, device, equipment and medium for low-dose PET image reconstruction based on the gradient domain, aiming to solve the problem that the low-dose PET image cannot be provided due to the fact that the prior art cannot provide an effective low-dose PET image reconstruction method The problem of slow reconstruction speed and poor reconstruction image quality.
  • the present invention provides a gradient-domain low-dose PET image reconstruction method, which includes the following steps:
  • the projection data and the system matrix perform image reconstruction on the pre-initialized PET image to be reconstructed through a preset PET image reconstruction algorithm to obtain an 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 using Lagrange multiplication to obtain the target reconstructed PET image corresponding to the initial reconstructed PET image.
  • the present invention provides a low-dose PET image reconstruction device based on the gradient domain, the device comprising:
  • the parameter acquisition unit is used to acquire projection data acquired by the PET device and acquire the system matrix of the PET device when receiving the reconstruction request of the low-dose PET image;
  • An initial reconstruction unit 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;
  • the reconstructed image obtaining unit is used to jointly optimize and solve the pre-constructed image reconstruction equation and the pre-constructed gradient domain image feature selection equation based on the initial reconstructed PET image, to obtain the initial reconstructed PET image
  • the corresponding target reconstructs the PET image.
  • the present invention also provides a computing device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, which is implemented when the processor executes the computer program
  • a computing device including a memory, a processor, and a computer program stored in the memory and executable on the processor, which is implemented when the processor executes the computer program
  • the present invention also provides a computer-readable storage medium that stores a computer program, and when the computer program is executed by a processor, the low-dose PET image reconstruction based on the gradient domain as described above is realized. The steps described in the method.
  • the present invention reconstructs the pre-initialized PET image to be reconstructed by the PET image reconstruction algorithm to obtain an initial reconstructed PET image.
  • the Lager is used
  • the Lagrangian multiplication optimizes and solves 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 increasing the reconstruction speed of the low-dose PET image and reducing
  • the degree of artifacts in the reconstructed image further improves the image quality of low-dose PET image reconstruction.
  • FIG. 1 is an implementation flowchart of a gradient-based low-dose PET image reconstruction method provided in Embodiment 1 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 a preferred 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 a low-dose PET image reconstruction device based on a gradient domain provided by Embodiment 2 of the present invention.
  • FIG. 6 is a schematic structural diagram of a computing device according to Embodiment 3 of the present invention.
  • FIG. 1 shows an implementation flow of a low-dose PET image reconstruction method based on a gradient domain provided in Embodiment 1 of the present invention.
  • FIG. 1 shows an implementation flow of a low-dose PET image reconstruction method based on a gradient domain provided in Embodiment 1 of the present invention.
  • the details are as follows:
  • step S101 when a reconstruction request for a low-dose PET image is received, the projection data collected by the PET device is acquired, and the system matrix of the PET device is acquired.
  • the embodiments of the present invention are applicable to medical image processing platforms, systems or devices, such as personal computers and servers.
  • receive a request to reconstruct a low-dose PET image obtain the under-sampled projection data collected by the PET device under low-dose conditions, and obtain the PET device's system matrix, which is based on the PET device's geometric structure information Calculated.
  • step S102 according to the projection data and the system matrix, the pre-initialized PET image to be reconstructed is image-reconstructed by a preset PET image reconstruction algorithm to obtain an initial reconstructed PET image.
  • a predetermined number of iteration operations are performed on the pre-initialized PET image to be reconstructed through a preset PET image reconstruction algorithm to reconstruct the PET image to be reconstructed to obtain the initial reconstruction PET image, where the PET image to be reconstructed is a two-dimensional image, and the preset PET image reconstruction algorithm is Maximum Likelihood Expected Maximum Algorithm (Maximum Likelihood Expectation Maximized, MLEM for short) or Ordered Subset Expected Maximum Algorithm (Ordered Subset Expectation Maximum Maximization) , Referred to as OSEM) or Maximum Posterior Probability Algorithm (Maximum, Posterior, MAP).
  • the pixel values of the PET image to be reconstructed are all initialized to zero.
  • step S103 based on the initial reconstructed PET image, Lagrange multiplication is used to jointly optimize 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 .
  • control coefficient L of the sparsity of the feature vector is set to 5, so as to better reduce the noise of the PET image represented by the learned feature matrix and the sparsity of the feature vector.
  • Lagrange multiplication is used to jointly optimize the pre-built image reconstruction equation and the pre-built gradient domain image feature selection equation
  • the Lagrange equation is solved iteratively, which improves the reconstruction speed of PET images.
  • the Bregman iterative method is used to decompose the Lagrange equation into a gradient image update function, an iterative error correction function, a PET image reconstruction function, and a feature extraction function to update the gradient image update function, iterative error correction function, 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.
  • the feature extraction function obtained by decomposing the Lagrange equation is:
  • the obtained feature matrix D and feature vector ⁇ l are used as initial values for updating the gradient image ⁇ in the next iteration, thereby transforming the initial reconstructed PET image from the image domain to the gradient domain, and performing feature learning on the gradient domain image.
  • the initial reconstructed PET image is sparsely represented by the learned feature matrix and feature vector, thereby reducing the noise in the initial reconstructed PET image, and thereby improving the reconstruction effect of the subsequent PET image.
  • k is the current number of iterations.
  • the gradient image update function obtained by decomposing the Lagrange equation is:
  • the obtained gradient image ⁇ 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 reconstructions.
  • v 2 is the preset weight used to control the iteration error in the Bregman iteration
  • b is the error correction value of the Bregman iteration.
  • v 2 it is further preferred to set v 2 to 1, thereby further reducing the degree of artifacts of the target reconstructed PET image for subsequent reconstruction.
  • the iterative error correction function obtained by decomposing the Lagrange equation is used as an initial value for reconstructing the target reconstructed PET image m in the next iteration, thereby improving the image quality of the reconstructed PET image.
  • the PET image reconstruction function obtained by decomposing the Lagrange equation ⁇ k is the gradient image of the kth iteration, and b k is the error correction value of the kth iteration, thereby improving the image quality of the reconstructed PET image.
  • the Lagrange equation is iteratively solved using the Bregman iterative method through the following steps:
  • step S201 the gradient image corresponding to the initial reconstructed PET image is updated using the gradient image update function according to the preset initial feature matrix and the preset initial feature vector.
  • 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.
  • step S203 it is determined whether the current number of iterations reaches a preset iteration threshold.
  • step S204 when the current number of iterations reaches a preset iteration threshold (for example, 50 times), step S204 is executed; otherwise, jump to step S205.
  • a preset iteration threshold for example, 50 times
  • step S204 the target reconstructed PET image is output.
  • step S205 the target reconstructed PET image is set as the initial reconstructed PET image, and a corresponding number of image blocks are extracted from the gradient image corresponding to the initial reconstructed PET image according to the preset image block extraction matrix.
  • the gradient image includes a horizontal gradient image And vertical gradient image.
  • the initial reconstructed PET image is firstly converted from the image domain to the gradient domain to obtain a horizontal gradient image and a vertical gradient image.
  • the horizontal gradient image and the vertical gradient image are extracted respectively Corresponding number of horizontal image blocks and vertical image blocks.
  • 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.
  • feature learning is performed on the extracted horizontal image block and vertical image block, respectively, until the learned horizontal/vertical feature matrix corresponding to the horizontal/vertical gradient image and the horizontal/vertical feature corresponding to the horizontal/vertical image block
  • the vector satisfies the feature extraction function, where each column of the feature matrix corresponds one-to-one to the feature vector corresponding to each image block.
  • step S207 the feature matrix and the feature vector are set as the initial feature matrix and the initial feature vector, the current iteration number is increased by one, and the process jumps to step S201 to continue the next iteration to reconstruct the PET image.
  • an image reconstruction is performed on the PET image to be reconstructed in advance through the PET image reconstruction algorithm to obtain an initial reconstructed PET image, and the initial reconstructed PET image Image, using Lagrange multiplication to jointly optimize 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 low-dose PET image Reconstruction speed, and reduce the degree of artifacts in the reconstructed image, thereby improving the image quality of low-dose PET image reconstruction.
  • FIG. 3 shows a structure of a low-dose PET image reconstruction device based on a gradient domain provided by Embodiment 2 of the present invention. For ease of description, only parts related to the embodiment of the present invention are shown, including:
  • the parameter obtaining unit 31 is configured to obtain projection data collected by the PET device and obtain the system matrix of the PET device when receiving the reconstruction request of the low-dose PET image;
  • the initial reconstruction unit 32 is configured to perform image reconstruction on the pre-initialized PET image to be reconstructed according to the projection data and the system matrix through a preset PET image reconstruction algorithm to obtain an initial reconstructed PET image;
  • 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 by using Lagrange multiplication based on the initial reconstructed PET image to obtain the target corresponding to the initial reconstructed PET image Reconstruct the PET image.
  • the reconstructed image obtaining unit 33 includes:
  • the iterative solving unit 331 is used to iteratively solve the Lagrange equation by the image reconstruction equation and the gradient domain image feature selection equation using the Bregman iterative method.
  • the iterative solving unit 331 includes:
  • the equation decomposition unit 3311 is used to decompose the Lagrange equation 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 to update the gradient image function and 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.
  • the equation decomposition unit 3311 includes:
  • the gradient image update unit 51 is configured to update the gradient image corresponding to the initial 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 based on the updated gradient image and the error correction value obtained by the iterative error correction function to obtain the target reconstructed PET image;
  • the iteration number judgment unit 53 is used to judge whether the current iteration number reaches the preset iteration threshold
  • the PET image output unit 54 is used to output the target reconstructed PET image
  • the image block extraction unit 55 is used to otherwise set the target reconstructed PET image as the initial reconstructed PET image, and extract the corresponding number of image blocks from the gradient image corresponding to the initial reconstructed PET image according to the preset image block extraction matrix.
  • Images include horizontal gradient images and vertical gradient images;
  • the feature learning unit 56 is used to perform feature learning on the image block until the feature matrix corresponding to the gradient image obtained by learning and the feature vector corresponding to the image block satisfy the feature extraction function;
  • 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 iteration to reconstruct the PET image.
  • each unit of the low-dose PET image reconstruction device based on the gradient domain may be implemented by a corresponding hardware or software unit, and each unit may be an independent software and hardware unit, or may be integrated into one software and hardware unit. It is not used here to limit the invention. Specifically, for the implementation of each unit, reference may be made to the description of the foregoing first embodiment, and details are not described herein again.
  • FIG. 6 shows the structure of the computing device provided in Embodiment 3 of the present invention. For convenience 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 executable on the processor 60.
  • the processor 60 executes the computer program 62
  • the steps in the embodiment of the low-dose PET image reconstruction method based on the gradient domain are implemented, for example, steps S101 to S103 shown in FIG. 1.
  • the processor 60 executes the computer program 62
  • the functions of the units in the above device embodiments are realized, for example, the functions of the units 31 to 33 shown in FIG. 3.
  • an image reconstruction is performed on the PET image to be reconstructed in advance through the PET image reconstruction algorithm to obtain an initial reconstructed PET image, and the initial reconstructed PET image Image, using Lagrange multiplication to jointly optimize 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 low-dose PET image Reconstruction speed, and reduce the degree of artifacts in the reconstructed image, thereby improving the image quality of low-dose PET image reconstruction.
  • the computing device in this embodiment of the present invention may be a personal computer or a server.
  • the steps implemented by the processor 60 in the computing device 6 when the computer program 62 is executed to implement the low-dose PET image reconstruction method based on the gradient domain reference may be made to the description of the foregoing method embodiments, which will not be repeated here.
  • a computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the embodiment of the method for reconstructing the low-dose PET image based on the gradient domain is implemented.
  • the functions of the units in the foregoing device embodiments are realized, for example, the functions of the units 31 to 33 shown in FIG. 3.
  • an image reconstruction is performed on the PET image to be reconstructed in advance through the PET image reconstruction algorithm to obtain an initial reconstructed PET image, and the initial reconstructed PET image Image, using Lagrange multiplication to jointly optimize 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 low-dose PET image Reconstruction speed, and reduce the degree of artifacts in the reconstructed image, 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 capable of carrying computer program code, and a recording medium, such as ROM/RAM, magnetic disk, optical disk, flash memory, and other memories.

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Abstract

一种基于梯度域的低剂量PET图像重建方法、装置、设备及介质，该方法包括：根据PET设备采集到的投影数据以及该PET设备的系统矩阵，通过PET图像重建算法对预先初始化的待重建PET图像进行图像重建，获得初始重建PET图像（S102），根据初始重建PET图像，采用拉格朗日乘法将预先构建的图像重建方程和预先构建的梯度域图像特征选取方程进行联合优化求解，得到初始重建PET图像对应的目标重建PET图像（S103），从而提高了低剂量PET图像的重建速度，且降低重建图像的伪影程度，进而提高了低剂量PET图像重建的图像质量。

Description

基于梯度域的低剂量PET图像重建方法、装置、设备及介质 技术领域
本发明属于医学PET成像技术领域，尤其涉及一种基于梯度域的低剂量PET图像重建方法、装置、设备及介质。
背景技术
正电子发射断层成像(Positron Emission Tomography，简称PET)是一种发射型成像技术(Emission Tomography，简称ET)，它通过把放射性药物注入体内的方法来显示不同组织的新陈代谢情况。PET技术是继计算机断层成像(Computed Tomography，简称CT)和磁共振成像(Magnetic Resonance Imaging，简称MRI)之后应用于临床的一种新型影像技术，PET技术在肿瘤学、心血管疾病学、神经系统疾病研究、以及新药开发研究等领域中显示出卓越的性能。
在PET成像中，放射性药物实际上是个分子载体，它依附于特定的生理组织或病理过程。放射性物质在药物的带领下在人体内有目的的分布。PET成像的目的实际上就是得到放射性物质在人体内部的分布图，它的工作原理是：将一些放射性核元素，如O-15、C-11、N-13和F-18等标记在人体代谢所需的化合物上，然后通过手臂静脉血管注射等方式输入受检者体内。标记化合物在参与体内代谢的过程中，放射性核元素发生衰变，释放出正电子(带一个正电荷的电子)，正电子与其周围的(带负电)电子发生湮灭，产生两个能量为511keV的伽马光子。这对光子在一条直线上朝相反的方向射出，利用体外的伽马照相机可以探测到特定区域放射的所有光子，然后设计一定的算法，就可以近似得到放射性物质在人体内部的分布情况。
由于在PET检查中使用的放射性药物会对近距离接触该药物的人员产生辐射，而受到辐射的人员患癌的几率会远高于正常人，同时放射性药物的消耗在 PET检查的成本中占有一定比重。因此，根据国际放射防护委员会(International Commission on Radiological Protection，简称ICRP)提出的合理使用低剂量(As Low As Reasonably Achievable，简称ALARA)原则，在PET临床诊断时，以期用最小的剂量获得满足临床需求的图像，尽量降低对患者的辐射剂量。
然而，在对低剂量采样得到的测量数据进行PET图像重建时，现有传统的PET图像重建算法重建图像的速度慢，进而使得重建图像产生运动伪影，这些伪影将会直接影响医生的诊断行为。
发明内容
本发明的目的在于提供一种基于梯度域的低剂量PET图像重建方法、装置、设备及介质，旨在解决由于现有技术无法提供一种有效的低剂量PET图像重建方法，导致低剂量PET图像重建速度慢、且重建图像质量差的问题。
一方面，本发明提供了一种基于梯度域的低剂量PET图像重建方法，所述方法包括下述步骤：
当接收到低剂量PET图像的重建请求时，获取通过PET设备采集到的投影数据，并获取所述PET设备的系统矩阵；
根据所述投影数据以及所述系统矩阵，通过预设的PET图像重建算法对预先初始化的待重建PET图像进行图像重建，获得初始重建PET图像；
根据所述初始重建PET图像，采用拉格朗日乘法将预先构建的图像重建方程和预先构建的梯度域图像特征选取方程进行联合优化求解，得到所述初始重建PET图像对应的目标重建PET图像。
另一方面，本发明提供了一种基于梯度域的低剂量PET图像重建装置，所述装置包括：
参数获取单元，用于当接收到低剂量PET图像的重建请求时，获取通过PET设备采集到的投影数据，并获取所述PET设备的系统矩阵；
初始重建单元，用于根据所述投影数据以及所述系统矩阵，通过预设的PET图像重建算法对预先初始化的待重建PET图像进行图像重建，获得初始重建PET图像；以及
重建图像获得单元，用于根据所述初始重建PET图像，采用拉格朗日乘法将预先构建的图像重建方程和预先构建的梯度域图像特征选取方程进行联合优化求解，得到所述初始重建PET图像对应的目标重建PET图像。
另一方面，本发明还提供了一种计算设备，包括存储器、处理器以及存储在所述存储器中并可在所述处理器上运行的计算机程序，所述处理器执行所述计算机程序时实现如上述基于梯度域的低剂量PET图像重建方法所述的步骤。
另一方面，本发明还提供了一种计算机可读存储介质，所述计算机可读存储介质存储有计算机程序，所述计算机程序被处理器执行时实现如上述基于梯度域的低剂量PET图像重建方法所述的步骤。
本发明根据PET设备采集到的投影数据以及该PET设备的系统矩阵，通过PET图像重建算法对预先初始化的待重建PET图像进行图像重建，获得初始重建PET图像，根据初始重建PET图像，采用拉格朗日乘法将预先构建的图像重建方程和预先构建的梯度域图像特征选取方程进行联合优化求解，得到初始重建PET图像对应的目标重建PET图像，从而提高了低剂量PET图像的重建速度，且降低重建图像的伪影程度，进而提高了低剂量PET图像重建的图像质量。
附图说明
图1是本发明实施例一提供的基于梯度域的低剂量PET图像重建方法的实现流程图；
图2是本发明实施例一中采用Bregman迭代方法对拉格朗日方程进行迭代求解的实现流程图；
图3是本发明实施例二提供的基于梯度域的低剂量PET图像重建装置的结 构示意图；
图4是本发明实施例二提供的基于梯度域的低剂量PET图像重建装置的优选结构示意图；
图5是本发明实施例二提供的基于梯度域的低剂量PET图像重建装置的又一优选结构示意图；以及
图6是本发明实施例三提供的计算设备的结构示意图。
具体实施方式
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。
以下结合具体实施例对本发明的具体实现进行详细描述：
实施例一：
图1示出了本发明实施例一提供的基于梯度域的低剂量PET图像重建方法的实现流程，为了便于说明，仅示出了与本发明实施例相关的部分，详述如下：
在步骤S101中，当接收到低剂量PET图像的重建请求时，获取通过PET设备采集到的投影数据，并获取PET设备的系统矩阵。
本发明实施例适用于医学图像处理平台、系统或设备，例如个人计算机、服务器等。当接收到对低剂量PET图像进行重建的请求时，获取通过PET设备在低剂量条件下采集到的欠采样投影数据，并获取PET设备的系统矩阵，该系统矩阵是根据PET设备的几何结构信息计算得到的。
在步骤S102中，根据投影数据以及系统矩阵，通过预设的PET图像重建算法对预先初始化的待重建PET图像进行图像重建，获得初始重建PET图像。
在本发明实施例中，根据投影数据以及系统矩阵，通过预设的PET图像重建算法对预先初始化的待重建PET图像进行预设次数的迭代操作，以对待重建PET图像进行图像重建，获得初始重建PET图像，其中，待重建PET图像是 二维图像，预设的PET图像重建算法为最大似然期望最大算法(Maximum Likelihood Expectation Maximized，简称MLEM)或者有序子集期望值最大算法(Ordered Subset Expectation Maximization，简称OSEM)或者最大后验概率算法(Maximum A Posterior，MAP)。
在初始化待重建PET图像时，作为示例地，将待重建PET图像的像素值都初始化为零。
在步骤S103中，根据初始重建PET图像，采用拉格朗日乘法将预先构建的图像重建方程和预先构建的梯度域图像特征选取方程进行联合优化求解，得到初始重建PET图像对应的目标重建PET图像。
在本发明实施例中，采用拉格朗日乘法将预先构建的图像重建方程y u＝G um和预先构建的梯度域图像特征选取方程
Figure PCTCN2019071098-appb-000001
进行联立，得到对应的拉格朗日方程
Figure PCTCN2019071098-appb-000002
Figure PCTCN2019071098-appb-000003
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)，v 1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。
在本发明实施例中，优选地，将特征向量稀疏度的控制系数L设置为5，从而更好的降低通过学习到的特征矩阵和特征向量稀疏表示的PET图像的噪声。
在采用拉格朗日乘法将预先构建的图像重建方程和预先构建的梯度域图像 特征选取方程进行联合优化求解时，优选地，采用Bregman迭代方法对由图像重建方程和梯度域图像特征选取方程联立的拉格朗日方程进行迭代求解，从而提高了PET图像的重建速度。
进一步优选地，采用Bregman迭代方法将拉格朗日方程分解为梯度图像更新函数、迭代误差校正函数、PET图像重建函数、以及特征提取函数，以对梯度图像更新函数、迭代误差校正函数、PET图像重建函数、以及特征提取函数进行迭代求解，得到初始重建PET图像对应的目标重建PET图像，从而进一步提高了PET图像的重建速度，且提高重建得到的目标重建PET图像的图像质量。
优选地，对拉格朗日方程分解得到的特征提取函数为
Figure PCTCN2019071098-appb-000004
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。
优选地，对拉格朗日方程分解得到的梯度图像更新函数为
Figure PCTCN2019071098-appb-000005
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，v 2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。
在本发明实施例中，进一步优选地，将v 2设置为1，从而进一步降低后续重建的目标重建PET图像的伪影程度。
优选地，对拉格朗日方程分解得到的迭代误差校正函数
Figure PCTCN2019071098-appb-000006
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。
优选地，对拉格朗日方程分解得到的PET图像重建函数
Figure PCTCN2019071098-appb-000007
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。
如图2所示，优选地，通过下述步骤实现采用Bregman迭代方法对拉格朗日方程进行迭代求解：
在步骤S201中，根据预设的初始特征矩阵和预设的初始特征向量，使用梯度图像更新函数对初始重建PET图像对应的梯度图像进行更新。
在步骤S202中，根据更新后的梯度图像和迭代误差校正函数得到的误差校正值，使用PET图像重建函数将梯度图像从梯度域中恢复到图像域，得到目标重建PET图像。
在步骤S203中，判断当前迭代次数是否达到预设的迭代阈值。
在本发明实施例中，当当前迭代次数达到预设的迭代阈值(例如，50次)时，执行步骤S204，否则，跳转至步骤S205。
在步骤S204中，输出目标重建PET图像。
在步骤S205中，将目标重建PET图像设置为初始重建PET图像，并根据预设的图像块提取矩阵，从初始重建PET图像对应的梯度图像中提取对应数量的图像块，梯度图像包括水平梯度图像和垂直梯度图像。
在本发明实施例中，首先将初始重建PET图像从图像域转换到梯度域，得到水平梯度图像和垂直梯度图像，根据预设的图像块提取矩阵，分别从水平梯度图像和垂直梯度图像中提取对应数量的水平图像块和垂直图像块。
在步骤S206中，对图像块进行特征学习，直至学习得到的梯度图像对应的特征矩阵和图像块对应的特征向量满足特征提取函数。
在本发明实施例中，分别对提取到水平图像块和垂直图像块进行特征学习，直至学习得到的水平/垂直梯度图像对应的水平/垂直特征矩阵和水平/垂直图像块对应的水平/垂直特征向量满足特征提取函数，其中，特征矩阵的每一列与每 个图像块对应的特征向量一一对应。
在步骤S207中，将特征矩阵和特征向量分别设置为初始特征矩阵和初始特征向量，将当前迭代次数增加1次，并跳转至步骤S201，继续下一轮迭代，以重建PET图像。
通过上述步骤S201-步骤S207实现对拉格朗日方程进行迭代求解，以得到初始重建PET图像对应的目标重建PET图像，从而降低重建图像的伪影程度，提高了低剂量PET图像重建的图像质量。
在本发明实施例中，根据PET设备采集到的投影数据以及该PET设备的系统矩阵，通过PET图像重建算法对预先初始化的待重建PET图像进行图像重建，获得初始重建PET图像，根据初始重建PET图像，采用拉格朗日乘法将预先构建的图像重建方程和预先构建的梯度域图像特征选取方程进行联合优化求解，得到初始重建PET图像对应的目标重建PET图像，从而提高了低剂量PET图像的重建速度，且降低重建图像的伪影程度，进而提高了低剂量PET图像重建的图像质量。
实施例二：
图3示出了本发明实施例二提供的基于梯度域的低剂量PET图像重建装置的结构，为了便于说明，仅示出了与本发明实施例相关的部分，其中包括：
参数获取单元31，用于当接收到低剂量PET图像的重建请求时，获取通过PET设备采集到的投影数据，并获取PET设备的系统矩阵；
初始重建单元32，用于根据投影数据以及系统矩阵，通过预设的PET图像重建算法对预先初始化的待重建PET图像进行图像重建，获得初始重建PET图像；以及
重建图像获得单元33，用于根据初始重建PET图像，采用拉格朗日乘法将预先构建的图像重建方程和预先构建的梯度域图像特征选取方程进行联合优化求解，得到初始重建PET图像对应的目标重建PET图像。
如图4所示，优选地，重建图像获得单元33包括：
迭代求解单元331，用于采用Bregman迭代方法对由图像重建方程和梯度域图像特征选取方程联立的拉格朗日方程进行迭代求解。
进一步优选地，迭代求解单元331包括：
方程分解单元3311，用于采用Bregman迭代方法将拉格朗日方程分解为梯度图像更新函数、迭代误差校正函数、PET图像重建函数、以及特征提取函数，以对梯度图像更新函数、迭代误差校正函数、PET图像重建函数、以及特征提取函数进行迭代求解，得到初始重建PET图像对应的目标重建PET图像。
进一步优选地，如图5所示，方程分解单元3311包括：
梯度图像更新单元51，用于根据预设的初始特征矩阵和预设的初始特征向量，使用梯度图像更新函数对初始重建PET图像对应的梯度图像进行更新；
PET图像重建单元52，用于根据更新后的梯度图像和迭代误差校正函数得到的误差校正值，使用PET图像重建函数将梯度图像从梯度域中恢复到图像域，得到目标重建PET图像；
迭代次数判断单元53，用于判断当前迭代次数是否达到预设的迭代阈值；
PET图像输出单元54，用于是则，输出目标重建PET图像；
图像块提取单元55，用于否则，将目标重建PET图像设置为初始重建PET图像，并根据预设的图像块提取矩阵，从初始重建PET图像对应的梯度图像中提取对应数量的图像块，梯度图像包括水平梯度图像和垂直梯度图像；
特征学习单元56，用于对图像块进行特征学习，直至学习得到的梯度图像对应的特征矩阵和图像块对应的特征向量满足特征提取函数；以及
参数设置单元57，用于将特征矩阵和特征向量分别设置为初始特征矩阵和初始特征向量，并触发梯度图像更新单元51，继续下一轮迭代，以重建PET图像。
在本发明实施例中，基于梯度域的低剂量PET图像重建装置的各单元可由相应的硬件或软件单元实现，各单元可以为独立的软、硬件单元，也可以集成为一个软、硬件单元，在此不用以限制本发明。具体地，各单元的实施方式可 参考前述实施例一的描述，在此不再赘述。
实施例三：
图6示出了本发明实施例三提供的计算设备的结构，为了便于说明，仅示出了与本发明实施例相关的部分。
本发明实施例的计算设备6包括处理器60、存储器61以及存储在存储器61中并可在处理器60上运行的计算机程序62。该处理器60执行计算机程序62时实现上述基于梯度域的低剂量PET图像重建方法实施例中的步骤，例如图1所示的步骤S101至S103。或者，处理器60执行计算机程序62时实现上述各装置实施例中各单元的功能，例如图3所示单元31至33的功能。
在本发明实施例中，根据PET设备采集到的投影数据以及该PET设备的系统矩阵，通过PET图像重建算法对预先初始化的待重建PET图像进行图像重建，获得初始重建PET图像，根据初始重建PET图像，采用拉格朗日乘法将预先构建的图像重建方程和预先构建的梯度域图像特征选取方程进行联合优化求解，得到初始重建PET图像对应的目标重建PET图像，从而提高了低剂量PET图像的重建速度，且降低重建图像的伪影程度，进而提高了低剂量PET图像重建的图像质量。
本发明实施例的计算设备可以为个人计算机、服务器。该计算设备6中处理器60执行计算机程序62时实现基于梯度域的低剂量PET图像重建方法时实现的步骤可参考前述方法实施例的描述，在此不再赘述。
实施例四：
在本发明实施例中，提供了一种计算机可读存储介质，该计算机可读存储介质存储有计算机程序，该计算机程序被处理器执行时实现上述基于梯度域的低剂量PET图像重建方法实施例中的步骤，例如，图1所示的步骤S101至S103。或者，该计算机程序被处理器执行时实现上述各装置实施例中各单元的功能，例如图3所示单元31至33的功能。
在本发明实施例中，根据PET设备采集到的投影数据以及该PET设备的 系统矩阵，通过PET图像重建算法对预先初始化的待重建PET图像进行图像重建，获得初始重建PET图像，根据初始重建PET图像，采用拉格朗日乘法将预先构建的图像重建方程和预先构建的梯度域图像特征选取方程进行联合优化求解，得到初始重建PET图像对应的目标重建PET图像，从而提高了低剂量PET图像的重建速度，且降低重建图像的伪影程度，进而提高了低剂量PET图像重建的图像质量。
本发明实施例的计算机可读存储介质可以包括能够携带计算机程序代码的任何实体或装置、记录介质，例如，ROM/RAM、磁盘、光盘、闪存等存储器。
以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。

Claims (14)

  1. 一种基于梯度域的低剂量PET图像重建方法，其特征在于，所述方法包括下述步骤：
    当接收到低剂量PET图像的重建请求时，获取通过PET设备采集到的投影数据，并获取所述PET设备的系统矩阵；
    根据所述投影数据以及所述系统矩阵，通过预设的PET图像重建算法对预先初始化的待重建PET图像进行图像重建，获得初始重建PET图像；
    根据所述初始重建PET图像，采用拉格朗日乘法将预先构建的图像重建方程和预先构建的梯度域图像特征选取方程进行联合优化求解，得到所述初始重建PET图像对应的目标重建PET图像。
  2. 如权利要求1所述的方法，其特征在于，采用拉格朗日乘法将预先构建的图像重建方程和预先构建的梯度域图像特征选取方程进行联合优化求解的步骤，包括：
    采用Bregman迭代方法对由所述图像重建方程和所述梯度域图像特征选取方程联立的拉格朗日方程进行迭代求解。
  3. 如权利要求2所述的方法，其特征在于，采用Bregman迭代方法对所述拉格朗日方程进行迭代求解的步骤，包括：
    采用Bregman迭代方法将所述拉格朗日方程分解为梯度图像更新函数、迭代误差校正函数、PET图像重建函数、以及特征提取函数，以对梯度图像更新函数、迭代误差校正函数、PET图像重建函数、以及特征提取函数进行迭代求解，得到所述初始重建PET图像对应的目标重建PET图像。
  4. 如权利要求3所述的方法，其特征在于，采用Bregman迭代方法对所述拉格朗日方程进行迭代求解的步骤，包括：
    根据预设的初始特征矩阵和预设的初始特征向量，使用所述梯度图像更新函数对所述初始重建PET图像对应的梯度图像进行更新；
    根据更新后的所述梯度图像和所述迭代误差校正函数得到的误差校正值， 使用所述PET图像重建函数将所述梯度图像从梯度域中恢复到图像域，得到目标重建PET图像；
    判断当前迭代次数是否达到预设的迭代阈值；
    是则，输出所述目标重建PET图像；
    否则，将所述目标重建PET图像设置为所述初始重建PET图像，并根据预设的图像块提取矩阵，从所述初始重建PET图像对应的梯度图像中提取对应数量的图像块，所述梯度图像包括水平梯度图像和垂直梯度图像；
    对所述图像块进行特征学习，直至学习得到的所述梯度图像对应的特征矩阵和所述图像块对应的特征向量满足所述特征提取函数；
    将所述特征矩阵和所述特征向量分别设置为所述初始特征矩阵和所述初始特征向量，并跳转至使用所述梯度图像更新函数对所述梯度图像进行更新的步骤。
  5. 如权利要求3所述的方法，其特征在于，所述特征提取函数为
    Figure PCTCN2019071098-appb-100001
    且s.t.||α l|| 0≤L，其中，R l为所述图像块提取矩阵，即根据所述R l从所述梯度图像ω中提取l个图像块，D为所述特征矩阵，α l为第l个图像块对应的特征向量，ω (i)表示所述初始重建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表示对所述特征向量的稀疏度的控制系数，k为所述当前迭代次数。
  6. 如权利要求3所述的方法，其特征在于，所述梯度图像更新函数
    Figure PCTCN2019071098-appb-100002
    其中，v 2表示Bregman迭代中控制迭代误差的权重，b为Bregman迭代的误差校正值。
  7. 如权利要求3所述的方法，其特征在于，所述迭代误差校正函数
    Figure PCTCN2019071098-appb-100003
  8. 如权利要求3所述的方法，其特征在于，所述PET图像重建函数
    Figure PCTCN2019071098-appb-100004
    y u为所述投影数据，G u为所述系统矩阵，m为所述待重建PET图像,v 1为预设的权重参数，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。
  9. 一种基于梯度域的低剂量PET图像重建装置，其特征在于，所述装置包括：
    参数获取单元，用于当接收到低剂量PET图像的重建请求时，获取通过PET设备采集到的投影数据，并获取所述PET设备的系统矩阵；
    初始重建单元，用于根据所述投影数据以及所述系统矩阵，通过预设的PET图像重建算法对预先初始化的待重建PET图像进行图像重建，获得初始重建PET图像；以及
    重建图像获得单元，用于根据所述初始重建PET图像，采用拉格朗日乘法将预先构建的图像重建方程和预先构建的梯度域图像特征选取方程进行联合优化求解，得到所述初始重建PET图像对应的目标重建PET图像。
  10. 如权利要求9所述的装置，其特征在于，所述重建图像获得单元包括：
    迭代求解单元，用于采用Bregman迭代方法对由所述图像重建方程和所述梯度域图像特征选取方程联立的拉格朗日方程进行迭代求解。
  11. 如权利要求10所述的装置，其特征在于，所述迭代求解单元包括：
    方程分解单元，用于采用Bregman迭代方法将所述拉格朗日方程分解为梯度图像更新函数、迭代误差校正函数、PET图像重建函数、以及特征提取函数，以对梯度图像更新函数、迭代误差校正函数、PET图像重建函数、以及特征提取函数进行迭代求解，得到所述初始重建PET图像对应的目标重建PET图像。
  12. 如权利要求11所述的装置，其特征在于，所述方程分解单元包括：
    梯度图像更新单元，用于根据预设的初始特征矩阵和预设的初始特征向量，使用所述梯度图像更新函数对所述初始重建PET图像对应的梯度图像进行更新；
    PET图像重建单元，用于根据更新后的所述梯度图像和所述迭代误差校正 函数得到的误差校正值，使用所述PET图像重建函数将所述梯度图像从梯度域中恢复到图像域，得到目标重建PET图像；
    迭代次数判断单元，用于判断当前迭代次数是否达到预设的迭代阈值；
    PET图像输出单元，用于是则，输出所述目标重建PET图像；
    图像块提取单元，用于否则，将所述目标重建PET图像设置为所述初始重建PET图像，并根据预设的图像块提取矩阵，从所述初始重建PET图像对应的梯度图像中提取对应数量的图像块，所述梯度图像包括水平梯度图像和垂直梯度图像；
    特征学习单元，用于对所述图像块进行特征学习，直至学习得到的所述梯度图像对应的特征矩阵和所述图像块对应的特征向量满足所述特征提取函数；以及
    参数设置单元，用于将所述特征矩阵和所述特征向量分别设置为所述初始特征矩阵和所述初始特征向量，并触发所述梯度图像更新单元执行使用所述梯度图像更新函数对所述梯度图像进行更新的步骤。
  13. 一种计算设备，包括存储器、处理器以及存储在所述存储器中并可在所述处理器上运行的计算机程序，其特征在于，所述处理器执行所述计算机程序时实现如权利要求1至8任一项所述方法的步骤。
  14. 一种计算机可读存储介质，所述计算机可读存储介质存储有计算机程序，其特征在于，所述计算机程序被处理器执行时实现如权利要求1至8任一项所述方法的步骤。
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