WO2020019684A1 - 低剂量pet图像重建方法、装置、设备及存储介质 - Google Patents

低剂量pet图像重建方法、装置、设备及存储介质 Download PDF

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WO2020019684A1
WO2020019684A1 PCT/CN2019/071087 CN2019071087W WO2020019684A1 WO 2020019684 A1 WO2020019684 A1 WO 2020019684A1 CN 2019071087 W CN2019071087 W CN 2019071087W WO 2020019684 A1 WO2020019684 A1 WO 2020019684A1
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image
pet
reconstructed
gradient
pet image
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胡战利
杨永峰
梁栋
刘新
郑海荣
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Shenzhen Institute of Advanced Technology of CAS
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    • G06T12/00—Tomographic reconstruction from projections

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  • the invention belongs to the field of PET imaging technology, and particularly relates to a method, a device, a device, and a storage medium for reconstructing a low-dose PET image.
  • PET Positron Tomography
  • CT Computed Tomography
  • MRI Magnetic Resonance Imaging
  • a radiopharmaceutical is actually a molecular carrier that is attached to a specific physiological tissue or pathological process. Radioactive substances are purposefully distributed in the human body under the guidance of drugs.
  • the purpose of PET imaging is actually to obtain a distribution map of radioactive materials inside 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 human metabolism. The desired compound is then injected into the subject through a vein injection in the arm.
  • the radioactive nuclear element decays, releasing a positron (an electron with a positive charge), the positron and its surrounding (negatively charged) electrons are annihilated, and two gamma energies of 511 keV are generated.
  • Horse photon The pair of photons are emitted in opposite directions on a straight line.
  • a certain algorithm can be designed to approximate the distribution of the radioactive material inside the human body.
  • the purpose of the present invention is to provide a low-dose PET image reconstruction method, device, equipment and storage medium, which aims to solve the problem that the low-dose PET image reconstruction speed is slow due to the inability to provide an effective low-dose PET image reconstruction method in the prior art. And poor reconstruction image quality.
  • the present invention provides a low-dose PET image reconstruction method, which includes the following steps:
  • the image reconstruction algorithm performs image reconstruction on a PET image to be reconstructed in advance.
  • the present invention provides a low-dose PET image reconstruction device, which includes:
  • a parameter obtaining unit configured to obtain projection data collected by a PET device when a request for reconstruction of a low-dose PET image is received, and obtain a system matrix of the PET device;
  • 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;
  • a gradient image acquisition unit configured to perform a gradient operation on the initial reconstructed PET image to obtain a horizontal gradient image and a vertical gradient image corresponding to the initial reconstructed PET image;
  • a dictionary learning unit configured to perform dictionary learning on the horizontal gradient image and the vertical gradient image, respectively, to obtain a corresponding sparse representation of the horizontal gradient image and a sparse representation of the vertical gradient image;
  • a reconstructed image acquisition unit configured to restore the horizontal gradient image sparse representation and the vertical gradient image sparse representation from a gradient domain to an image domain by a least square method to obtain a reconstructed PET image
  • a reconstructed image judging unit is configured to judge whether the reconstructed PET image meets a preset objective function, and if so, output the reconstructed PET image, otherwise, set the reconstructed PET image as the PET image to be reconstructed and trigger
  • the initial reconstruction unit performs a step of performing image reconstruction on a pre-initialized PET image to be reconstructed through a preset PET image reconstruction algorithm.
  • 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.
  • the processor is implemented when the processor executes the computer program.
  • the present invention also provides a computer-readable storage medium, where the computer-readable storage medium stores a computer program that, when executed by a processor, implements the method described in the above-mentioned low-dose PET image reconstruction method. step.
  • the PET image reconstruction algorithm is used to reconstruct the PET image to be reconstructed to obtain an initial reconstructed PET image.
  • the horizontal gradient corresponding to the initial reconstructed PET image is obtained.
  • Image sparse representation and vertical gradient image sparse representation restore horizontal gradient image sparse representation and vertical gradient image sparse representation from the gradient domain to the image domain, obtain the reconstructed PET image, determine whether the reconstructed PET image meets the objective function, and then output the reconstructed PET image Otherwise, continue to perform image reconstruction, gradient operation, and dictionary learning operations on the reconstructed PET image, thereby improving the reconstruction speed of the low-dose PET image and reducing the degree of artifacts in the reconstructed image, thereby improving the image reconstructed by the low-dose PET image. quality.
  • FIG. 1 is an implementation flowchart of a low-dose PET image reconstruction method provided by Embodiment 1 of the present invention
  • FIG. 2 is a schematic structural diagram of a low-dose PET image reconstruction device provided in Embodiment 2 of the present invention.
  • FIG. 3 is a schematic diagram of a preferred structure of a low-dose PET image reconstruction device provided in Embodiment 2 of the present invention.
  • FIG. 4 is a schematic structural diagram of a computing device according to a third embodiment of the present invention.
  • FIG. 1 shows the implementation process of the low-dose PET image reconstruction method provided in Embodiment 1 of the present invention.
  • the details are as follows:
  • step S101 when a request for reconstruction of a low-dose PET image is received, projection data collected by the PET device is acquired, and a system matrix of the PET device is acquired.
  • the embodiments of the present invention are applicable to a medical image processing platform, system, or device, such as a personal computer, a server, and the like.
  • a medical image processing platform, system, or device such as a personal computer, a server, and the like.
  • step S102 according to the projection data and the system matrix, an image reconstruction is performed on a pre-initialized PET image to be reconstructed through a preset PET image reconstruction algorithm to obtain an initial reconstructed PET image.
  • a preset number of iterative operations are performed on the pre-initialized PET image to be reconstructed through a preset PET image reconstruction algorithm to perform image reconstruction on the PET image to be reconstructed to obtain an initial reconstruction.
  • PET image where the PET image to be reconstructed is a two-dimensional image, and the preset PET image reconstruction algorithm is a Maximum Likelihood Expectation Maximum (MLEM) or Ordered Subset Expectation Maximum Maximization , Abbreviated as OSEM) or Maximum Posterior Probability Algorithm (Maximum APosterior, MAP).
  • the pixel values of the PET image to be reconstructed are all initialized to zero.
  • step S103 a gradient operation is performed on the initial reconstructed PET image to obtain a horizontal gradient image and a vertical gradient image corresponding to the initial reconstructed PET image.
  • the gradient operation is performed on the initial reconstructed PET image according to a preset vertical gradient image formula to obtain a vertical gradient image corresponding to the initial reconstructed PET image.
  • the horizontal gradient image formula is The vertical gradient image formula is For the initial reconstruction of the PET image, j and k are The coordinates of the middle pixel, thereby transforming the initial reconstructed PET image from the image domain to the gradient domain through the gradient operation, which improves the sparseness of the initial reconstructed PET image and further improves the imaging effect of subsequent PET image reconstruction.
  • step S104 dictionary learning is performed on the horizontal gradient image and the vertical gradient image, respectively, to obtain a corresponding sparse representation of the horizontal gradient image and a sparse representation of the vertical gradient image.
  • dictionary learning is performed on the horizontal gradient image and the vertical gradient image respectively to obtain the corresponding sparse representation of the horizontal gradient image and the sparse representation of the vertical gradient image. Due to the correlation between the neighboring pixel values of the medical image, the conversion to the gradient Images in the domain are more sparse than images in the image domain. Therefore, dictionary learning of images in the gradient domain is more sparse than image learning in the image domain to obtain a more sparse representation of the image, which improves subsequent PET image reconstruction. Imaging effect.
  • the dictionary learning is performed by a preset dictionary training algorithm (for example, K-SVD algorithm) according to the horizontal gradient image and the vertical gradient image, and then the learning ends according to the learning To update the sparse representation of the horizontal gradient image and the sparse representation of the vertical gradient image, thereby improving the imaging effect of subsequent PET image reconstruction.
  • a preset dictionary training algorithm for example, K-SVD algorithm
  • the horizontal gradient image and the vertical gradient image it is further preferred to perform image block extraction on the horizontal gradient image and the vertical gradient image according to a preset number of image blocks to obtain corresponding horizontal gradient image blocks and vertical gradient images.
  • Block to perform dictionary learning on the horizontal gradient image block and the vertical gradient image block to obtain the sparse representation corresponding to the horizontal gradient image block and the sparse representation corresponding to the vertical gradient image block.
  • the sparse representation corresponding to the horizontal gradient image block forms the sparse representation of the horizontal gradient image.
  • the sparse representation of the vertical gradient image is composed of the sparse representation corresponding to the vertical gradient image block, so that the sparse representation of the global image is converted into a sparse representation based on the image block through an adaptive dictionary, which effectively captures the local features of the initial reconstructed PET image and removes The artifacts and block effects of this image improve the imaging effect of subsequent PET image reconstruction.
  • step S105 the sparse representation of the horizontal gradient image and the sparse representation of the vertical gradient image are restored from the gradient domain to the image domain by the least square method, and a reconstructed PET image is obtained.
  • the sparse representation of the horizontal gradient image and the sparse representation of the vertical gradient image are fused by the least square method to restore the initial reconstructed PET image from the gradient domain to the image domain to obtain a reconstructed PET image.
  • step S106 it is determined whether the reconstructed PET image satisfies a preset objective function.
  • step S107 a reconstructed PET image is output.
  • step S108 the reconstructed PET image is set as the PET image to be reconstructed.
  • step S107 when the reconstructed PET image satisfies a preset objective function, step S107 is performed to end the reconstruction process of the PET image.
  • step S108 is performed, and jump is performed. Go to step S102 to perform image reconstruction on the PET image to be reconstructed by using a preset PET image reconstruction algorithm.
  • the objective function is expressed as:
  • g is the projection data
  • M is the system matrix
  • f is the PET image to be reconstructed
  • v 1 is a preset penalty parameter greater than 0.
  • a difference operator representing the horizontal and vertical directions
  • a gradient image representing f with Representing the horizontal gradient image and vertical gradient image of f
  • D is a preset over-complete dictionary
  • ⁇ l is the sparse coefficient corresponding to the l-th image block
  • T 0 is the sparseness of each image block.
  • the sparse transform algorithm combined with the iterative reconstruction algorithm achieves the continuous approximation of the reconstructed image to the real image, thereby reducing the dose of radiopharmaceuticals used in PET inspection and improving the imaging effect of PET image reconstruction.
  • a PET image reconstruction algorithm is used to reconstruct the PET image to be reconstructed, and an initial reconstructed PET image is obtained.
  • the gradient reconstruction and dictionary learning are used to obtain the initial reconstructed PET, respectively.
  • the sparse representation of the horizontal gradient image and the sparse representation of the vertical gradient image corresponding to the image restore the sparse representation of the horizontal gradient image and the sparse representation of the vertical gradient image from the gradient domain to the image domain, obtain a reconstructed PET image, and determine whether the reconstructed PET image satisfies the objective function. Then the reconstructed PET image is output.
  • the image reconstruction, gradient operation, and dictionary learning operations on the reconstructed PET image are continued, thereby improving the reconstruction speed of the low-dose PET image and reducing the degree of artifacts in the reconstructed image, thereby increasing the low-dose Image quality for PET image reconstruction.
  • FIG. 2 shows the structure of a low-dose PET image reconstruction device provided in Embodiment 2 of the present invention. For ease of description, only parts related to the embodiment of the present invention are shown, including:
  • a parameter obtaining unit 21 is configured to obtain projection data collected by a PET device when a request for reconstruction of a low-dose PET image is received, and obtain a system matrix of the PET device.
  • the embodiments of the present invention are applicable to a medical image processing platform, system, or device, such as a personal computer, a server, and the like.
  • a medical image processing platform, system, or device such as a personal computer, a server, and the like.
  • An initial reconstruction unit 22 is 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.
  • a preset number of iterative operations are performed on the pre-initialized PET image to be reconstructed through a preset PET image reconstruction algorithm to perform image reconstruction on the PET image to be reconstructed to obtain an initial reconstruction.
  • PET image where the PET image to be reconstructed is a two-dimensional image, and the preset PET image reconstruction algorithm is a Maximum Likelihood Expectation Maximum (MLEM) or Ordered Subset Expectation Maximum Maximization , Abbreviated as OSEM) or Maximum Posterior Probability Algorithm (Maximum APosterior, MAP).
  • the pixel values of the PET image to be reconstructed are all initialized to zero.
  • the gradient image acquisition unit 23 is configured to perform a gradient operation on the initial reconstructed PET image to obtain a horizontal gradient image and a vertical gradient image corresponding to the initial reconstructed PET image.
  • the present invention when performing a gradient operation on the initial reconstructed PET image, preferably, performing a gradient operation on the initial reconstructed PET image according to a preset horizontal gradient image formula to obtain a horizontal gradient image corresponding to the initial reconstructed PET image.
  • the gradient operation is performed on the initial reconstructed PET image according to a preset vertical gradient image formula to obtain a vertical gradient image corresponding to the initial reconstructed PET image.
  • the horizontal gradient image formula is The vertical gradient image formula is For the initial reconstruction of the PET image, j and k are The coordinates of the middle pixel, thereby transforming the initial reconstructed PET image from the image domain to the gradient domain through the gradient operation, which improves the sparseness of the initial reconstructed PET image and further improves the imaging effect of subsequent PET image reconstruction.
  • the dictionary learning unit 24 is configured to perform dictionary learning on the horizontal gradient image and the vertical gradient image, respectively, to obtain a corresponding sparse representation of the horizontal gradient image and a sparse representation of the vertical gradient image.
  • dictionary learning is performed on the horizontal gradient image and the vertical gradient image respectively to obtain the corresponding sparse representation of the horizontal gradient image and the sparse representation of the vertical gradient image. Due to the correlation between the neighboring pixel values of the medical image, the conversion to the gradient Images in the domain are more sparse than images in the image domain. Therefore, dictionary learning of images in the gradient domain is more sparse than image learning in the image domain to obtain a more sparse representation of the image, which improves subsequent PET image reconstruction. Imaging effect.
  • the dictionary learning is performed by a preset dictionary training algorithm (for example, K-SVD algorithm) according to the horizontal gradient image and the vertical gradient image, and then the learning ends according to the learning To update the sparse representation of the horizontal gradient image and the sparse representation of the vertical gradient image, thereby improving the imaging effect of subsequent PET image reconstruction.
  • a preset dictionary training algorithm for example, K-SVD algorithm
  • the horizontal gradient image and the vertical gradient image it is further preferred to perform image block extraction on the horizontal gradient image and the vertical gradient image according to a preset number of image blocks to obtain corresponding horizontal gradient image blocks and vertical gradient images.
  • Block to perform dictionary learning on the horizontal gradient image block and the vertical gradient image block to obtain the sparse representation corresponding to the horizontal gradient image block and the sparse representation corresponding to the vertical gradient image block.
  • the sparse representation corresponding to the horizontal gradient image block forms the sparse representation of the horizontal gradient image.
  • the sparse representation of the vertical gradient image is composed of the sparse representation corresponding to the vertical gradient image block, so that the sparse representation of the global image is converted into a sparse representation based on the image block through an adaptive dictionary, which effectively captures the local features of the initial reconstructed PET image and removes The artifacts and block effects of this image improve the imaging effect of subsequent PET image reconstruction.
  • the reconstructed image acquisition unit 25 is configured to recover the sparse representation of the horizontal gradient image and the sparse representation of the vertical gradient image from the gradient domain to the image domain by the least square method to obtain a reconstructed PET image.
  • the sparse representation of the horizontal gradient image and the sparse representation of the vertical gradient image are fused by the least square method to restore the initial reconstructed PET image from the gradient domain to the image domain to obtain a reconstructed PET image.
  • the reconstructed image determination unit 26 is configured to determine whether the reconstructed PET image satisfies a preset objective function. If yes, the reconstructed PET image is output. Otherwise, the reconstructed PET image is set as the PET image to be reconstructed, and the initial reconstruction unit 22 is triggered to execute. An image reconstruction step is performed on the PET image to be reconstructed through a preset PET image reconstruction algorithm.
  • the objective function is expressed as:
  • g is the projection data
  • M is the system matrix
  • f is the PET image to be reconstructed
  • v 1 is a preset penalty parameter greater than 0.
  • a difference operator representing the horizontal and vertical directions
  • a gradient image representing f with Representing the horizontal gradient image and vertical gradient image of f
  • D is a preset over-complete dictionary
  • ⁇ l is the sparse coefficient corresponding to the l-th image block
  • T 0 is the sparseness of each image block.
  • the sparse transform algorithm combined with the iterative reconstruction algorithm achieves the continuous approximation of the reconstructed image to the real image, thereby reducing the dose of radiopharmaceuticals used in PET inspection and improving the imaging effect of PET image reconstruction.
  • the gradient image acquisition unit 23 includes:
  • the gradient map acquisition subunit 231 is configured to perform a gradient operation on the initial reconstructed PET image according to a preset horizontal gradient image formula and a preset vertical gradient image formula to obtain a horizontal gradient image and a vertical gradient image corresponding to the initial reconstructed PET image.
  • the horizontal gradient image formula is
  • the vertical gradient image formula is For the initial reconstruction of the PET image, j and k are The coordinates of the pixel in.
  • the dictionary learning unit 24 includes:
  • An image block extraction unit 241 is configured to perform image block extraction on a horizontal gradient image and a vertical gradient image according to a preset number of image blocks to obtain corresponding horizontal gradient image blocks and vertical gradient image blocks;
  • a dictionary learning sub-unit 242 is configured to perform dictionary learning on the horizontal gradient image block and the vertical gradient image block, and obtain the corresponding horizontal gradient image sparse representation and the vertical gradient image sparse representation.
  • each unit of the low-dose PET image reconstruction device may be implemented by corresponding hardware or software units.
  • Each unit may be an independent software and hardware unit, or may be integrated into one software and hardware unit. Limit the invention.
  • FIG. 4 shows the structure of a computing device provided in 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 4 includes a processor 40, a memory 41, and a computer program 42 stored in the memory 41 and executable on the processor 40.
  • the processor 40 executes the computer program 42, the steps in the embodiment of the low-dose PET image reconstruction method described above are implemented, for example, steps S101 to S108 shown in FIG. 1.
  • the processor 40 executes the computer program 42, the functions of the units in the foregoing device embodiments are realized, for example, the functions of the units 21 to 26 shown in FIG. 2.
  • a PET image reconstruction algorithm is used to reconstruct the PET image to be reconstructed, and an initial reconstructed PET image is obtained.
  • the gradient reconstruction and dictionary learning are used to obtain the initial reconstructed PET, respectively.
  • the sparse representation of the horizontal gradient image and the sparse representation of the vertical gradient image corresponding to the image restore the sparse representation of the horizontal gradient image and the sparse representation of the vertical gradient image from the gradient domain to the image domain, obtain a reconstructed PET image, and determine whether the reconstructed PET image satisfies the objective function. Then the reconstructed PET image is output.
  • the image reconstruction, gradient operation, and dictionary learning operations on the reconstructed PET image are continued, thereby improving the reconstruction speed of the low-dose PET image and reducing the degree of artifacts in the reconstructed image, thereby increasing the low-dose Image quality for PET image reconstruction.
  • the computing device in the embodiment of the present invention may be a personal computer or a server.
  • the processor 40 in the computing device 4 executes the computer program 42 to implement the low-dose PET image reconstruction method, reference may be made to the description of the foregoing method embodiment, and details are not described herein again.
  • Embodiment 4 is a diagrammatic representation of Embodiment 4:
  • a computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps in the foregoing embodiment of the low-dose PET image reconstruction method. For example, steps S101 to S108 shown in FIG. 1.
  • the computer program when executed by a processor, the functions of the units in the foregoing device embodiments are implemented, for example, the functions of the units 21 to 26 shown in FIG. 2.
  • a PET image reconstruction algorithm is used to reconstruct the PET image to be reconstructed, and an initial reconstructed PET image is obtained.
  • the gradient reconstruction and dictionary learning are used to obtain the initial reconstructed PET, respectively.
  • the sparse representation of the horizontal gradient image and the sparse representation of the vertical gradient image corresponding to the image restore the sparse representation of the horizontal gradient image and the sparse representation of the vertical gradient image from the gradient domain to the image domain, obtain a reconstructed PET image, and determine whether the reconstructed PET image satisfies the objective function. Then the reconstructed PET image is output.
  • the image reconstruction, gradient operation, and dictionary learning operations on the reconstructed PET image are continued, thereby improving the reconstruction speed of the low-dose PET image and reducing the degree of artifacts in the reconstructed image, thereby increasing the low-dose Image quality for PET image reconstruction.
  • the computer-readable storage medium of the embodiment of the present invention may include any entity or device capable of carrying computer program code, a recording medium, for example, a memory such as a ROM / RAM, a magnetic disk, an optical disk, a flash memory, or the like.
  • a recording medium for example, a memory such as a ROM / RAM, a magnetic disk, an optical disk, a flash memory, or the like.

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Abstract

一种低剂量PET图像重建方法、装置、设备及存储介质，适用PET成像技术领域，该方法包括：根据采集到的投影数据和PET设备的系统矩阵，通过PET图像重建算法对待重建PET图像进行重建，获得初始重建PET图像，通过梯度运算和字典学习，分别获得初始重建PET图像对应的水平梯度图像稀疏表示和垂直梯度图像稀疏表示，将水平梯度图像稀疏表示和垂直梯度图像稀疏表示从梯度域恢复到图像域，获得重建PET图像，判断重建PET图像是否满足目标函数，是则输出重建PET图像，否则，继续对待重建PET图像执行图像重建、梯度运算以及字典学习的操作，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

低剂量PET图像重建方法、装置、设备及存储介质 技术领域
本发明属于PET成像技术领域，尤其涉及一种低剂量PET图像重建方法、装置、设备及存储介质。
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。
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低剂量PET图像重建方法、装置、设备及存储介质，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，本发明提供了一种低剂量PET图像重建方法，所述方法包括下述步骤：
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；
对所述初始重建PET图像进行梯度运算，获得所述初始重建PET图像对应的水平梯度图像和垂直梯度图像；
对所述水平梯度图像和所述垂直梯度图像分别进行字典学习，获得对应的水平梯度图像稀疏表示和垂直梯度图像稀疏表示；
通过最小二乘法将所述水平梯度图像稀疏表示和所述垂直梯度图像稀疏表示从梯度域恢复到图像域，获得重建PET图像；
判断所述重建PET图像是否满足预设的目标函数，是则，输出所述重建PET图像，否则，将所述重建PET图像设置为所述待重建PET图像，并跳转 到通过预设的PET图像重建算法对预先初始化的待重建PET图像进行图像重建的步骤。
另一方面，本发明提供了一种低剂量PET图像重建装置，所述装置包括：
参数获取单元，用于当接收到对低剂量PET图像进行重建的请求时，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；
梯度图像获取单元，用于对所述初始重建PET图像进行梯度运算，获得所述初始重建PET图像对应的水平梯度图像和垂直梯度图像；
字典学习单元，用于对所述水平梯度图像和所述垂直梯度图像分别进行字典学习，获得对应的水平梯度图像稀疏表示和垂直梯度图像稀疏表示；
重建图像获取单元，用于通过最小二乘法将所述水平梯度图像稀疏表示和所述垂直梯度图像稀疏表示从梯度域恢复到图像域，获得重建PET图像；以及
重建图像判断单元，用于判断所述重建PET图像是否满足预设的目标函数，是则，输出所述重建PET图像，否则，将所述重建PET图像设置为所述待重建PET图像，并触发所述初始重建单元执行通过预设的PET图像重建算法对预先初始化的待重建PET图像进行图像重建的步骤。
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低剂量PET图像重建方法所述的步骤。
本发明根据采集到的投影数据和PET设备的系统矩阵，通过PET图像重建算法对待重建PET图像进行重建，获得初始重建PET图像，通过梯度运算和 字典学习，分别获得初始重建PET图像对应的水平梯度图像稀疏表示和垂直梯度图像稀疏表示，将水平梯度图像稀疏表示和垂直梯度图像稀疏表示从梯度域恢复到图像域，获得重建PET图像，判断重建PET图像是否满足目标函数，是则输出重建PET图像，否则，继续对待重建PET图像执行图像重建、梯度运算以及字典学习的操作，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是本发明实施例二提供的低剂量PET图像重建装置的结构示意图；
图3是本发明实施例二提供的低剂量PET图像重建装置的优选结构示意图；以及
图4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，当接收到对低剂量PET图像进行重建的请求时，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，对初始重建PET图像进行梯度运算，获得初始重建PET图像对应的水平梯度图像和垂直梯度图像。
在本发明实施例中，在对初始重建PET图像进行梯度运算时，优选地，根据预设的水平梯度图像公式对初始重建PET图像进行梯度运算，获得该初始重建PET图像对应的水平梯度图像，根据预设的垂直梯度图像公式对初始重建PET图像进行梯度运算，获得该初始重建PET图像对应的垂直梯度图像，其中，水平梯度图像公式为
Figure PCTCN2019071087-appb-000001
垂直梯度图像公式为
Figure PCTCN2019071087-appb-000002
Figure PCTCN2019071087-appb-000003
为初始重建PET图像，j和k分别为
Figure PCTCN2019071087-appb-000004
中像素的坐标，从而通过梯度运算将初始重建PET图像从图像域转换到梯度域，提高了初始重建PET图像的稀疏性，进而提高后续PET图像重建的成像效果。
在对初始重建PET图像进行梯度运算之前，优选地，对重建得到的初始重建PET图像进行正约束，从而提高后续PET图像重建的成像效果。
在步骤S104中，对水平梯度图像和垂直梯度图像分别进行字典学习，获得 对应的水平梯度图像稀疏表示和垂直梯度图像稀疏表示。
在本发明实施例中，对水平梯度图像和垂直梯度图像分别进行字典学习，获得对应的水平梯度图像稀疏表示和垂直梯度图像稀疏表示，由于医学图像的近邻像素值具有相关性，即转换至梯度域中的图像比图像域中的图像更稀疏，因此，对梯度域中的图像进行字典学习比对图像域中的图像进行字典学习，可以获得更稀疏的图像稀疏表示，从而提高后续PET图像重建的成像效果。
在对水平梯度图像和垂直梯度图像分别进行字典学习时，优选地，根据水平梯度图像和垂直梯度图像，通过预设的字典训练算法(例如，K-SVD算法)进行字典学习，再根据学习结束的字典，对水平梯度图像稀疏表示和垂直梯度图像稀疏表示进行更新，从而提高后续PET图像重建的成像效果。
在对水平梯度图像和垂直梯度图像分别进行字典学习时，进一步优选地，根据预设的图像块数量对水平梯度图像和垂直梯度图像进行图像块提取，得到对应的水平梯度图像块和垂直梯度图像块，对水平梯度图像块和垂直梯度图像块进行字典学习，获得水平梯度图像块对应的稀疏表示和垂直梯度图像块对应的稀疏表示，由水平梯度图像块对应的稀疏表示构成水平梯度图像稀疏表示，由垂直梯度图像块对应的稀疏表示构成垂直梯度图像稀疏表示，从而通过自适应字典将全局图像的稀疏表示转换成基于图像块的稀疏表述，有效地捕捉初始重建PET图像的局部特征，并去除该图像的伪影和块效应，提高后续PET图像重建的成像效果。
在步骤S105中，通过最小二乘法将水平梯度图像稀疏表示和垂直梯度图像稀疏表示从梯度域恢复到图像域，获得重建PET图像。
在本发明实施例中，通过最小二乘法将水平梯度图像稀疏表示和垂直梯度图像稀疏表示进行融合，以将初始重建PET图像从梯度域恢复到图像域，获得重建PET图像。
在步骤S106中，判断重建PET图像是否满足预设的目标函数。
在步骤S107中，输出重建PET图像。
在步骤S108中，将重建PET图像设置为待重建PET图像。
在本发明实施例中，当重建PET图像满足预设的目标函数时，执行步骤S107，结束PET图像的重建过程，当重建PET图像不满足预设的目标函数时，执行步骤S108，并跳转到步骤S102执行通过预设的PET图像重建算法对待重建PET图像进行图像重建。
在本发明实施例中，优选地，目标函数表示为：
Figure PCTCN2019071087-appb-000005
其中，g为投影数据，M为系统矩阵，f为待重建PET图像，v 1为预设大于0的惩罚参数，
Figure PCTCN2019071087-appb-000006
和
Figure PCTCN2019071087-appb-000007
表示水平方向和垂直方向的差分算子，
Figure PCTCN2019071087-appb-000008
表示f的梯度图像，
Figure PCTCN2019071087-appb-000009
和
Figure PCTCN2019071087-appb-000010
分别表示f的水平梯度图像和垂直梯度图像，
Figure PCTCN2019071087-appb-000011
为从
Figure PCTCN2019071087-appb-000012
中提取出的第l个图像块的向量表示，D为预设的过完备字典，α l为第l个图像块所对应的稀疏系数，T 0为每个图像块的稀疏度，通过自适应稀疏变换算法结合迭代重建算法，来实现重建图像对真实图像的不断逼近，从而降低在PET检查中使用的放射性药物的剂量，并提高了PET图像重建的成像效果。
在本发明实施例中，根据采集到的投影数据和PET设备的系统矩阵，通过PET图像重建算法对待重建PET图像进行重建，获得初始重建PET图像，通过梯度运算和字典学习，分别获得初始重建PET图像对应的水平梯度图像稀疏表示和垂直梯度图像稀疏表示，将水平梯度图像稀疏表示和垂直梯度图像稀疏表示从梯度域恢复到图像域，获得重建PET图像，判断重建PET图像是否满足目标函数，是则输出重建PET图像，否则，继续对待重建PET图像执行图像重建、梯度运算以及字典学习的操作，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2示出了本发明实施例二提供的低剂量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21，用于当接收到对低剂量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。
初始重建单元22，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。
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。
梯度图像获取单元23，用于对初始重建PET图像进行梯度运算，获得初始重建PET图像对应的水平梯度图像和垂直梯度图像。
在本发明实施例中，在对初始重建PET图像进行梯度运算时，优选地，根据预设的水平梯度图像公式对初始重建PET图像进行梯度运算，获得该初始重建PET图像对应的水平梯度图像，根据预设的垂直梯度图像公式对初始重建PET图像进行梯度运算，获得该初始重建PET图像对应的垂直梯度图像，其中，水平梯度图像公式为
Figure PCTCN2019071087-appb-000013
垂直梯度图像公式为
Figure PCTCN2019071087-appb-000014
Figure PCTCN2019071087-appb-000015
为初始重建PET图像，j和k分别为
Figure PCTCN2019071087-appb-000016
中像素的坐标，从而通过梯度运算将初始重建PET图像从图像域转换到梯度域，提高了初始重建PET图像的稀疏性，进而提高后续PET图像重建的成像效果。
在对初始重建PET图像进行梯度运算之前，优选地，对重建得到的初始重建PET图像进行正约束，从而提高后续PET图像重建的成像效果。
字典学习单元24，用于对水平梯度图像和垂直梯度图像分别进行字典学习，获得对应的水平梯度图像稀疏表示和垂直梯度图像稀疏表示。
在本发明实施例中，对水平梯度图像和垂直梯度图像分别进行字典学习，获得对应的水平梯度图像稀疏表示和垂直梯度图像稀疏表示，由于医学图像的近邻像素值具有相关性，即转换至梯度域中的图像比图像域中的图像更稀疏，因此，对梯度域中的图像进行字典学习比对图像域中的图像进行字典学习，可以获得更稀疏的图像稀疏表示，从而提高后续PET图像重建的成像效果。
在对水平梯度图像和垂直梯度图像分别进行字典学习时，优选地，根据水平梯度图像和垂直梯度图像，通过预设的字典训练算法(例如，K-SVD算法)进行字典学习，再根据学习结束的字典，对水平梯度图像稀疏表示和垂直梯度图像稀疏表示进行更新，从而提高后续PET图像重建的成像效果。
在对水平梯度图像和垂直梯度图像分别进行字典学习时，进一步优选地，根据预设的图像块数量对水平梯度图像和垂直梯度图像进行图像块提取，得到对应的水平梯度图像块和垂直梯度图像块，对水平梯度图像块和垂直梯度图像块进行字典学习，获得水平梯度图像块对应的稀疏表示和垂直梯度图像块对应的稀疏表示，由水平梯度图像块对应的稀疏表示构成水平梯度图像稀疏表示，由垂直梯度图像块对应的稀疏表示构成垂直梯度图像稀疏表示，从而通过自适应字典将全局图像的稀疏表示转换成基于图像块的稀疏表述，有效地捕捉初始重建PET图像的局部特征，并去除该图像的伪影和块效应，提高后续PET图像重建的成像效果。
重建图像获取单元25，用于通过最小二乘法将水平梯度图像稀疏表示和垂 直梯度图像稀疏表示从梯度域恢复到图像域，获得重建PET图像。
在本发明实施例中，通过最小二乘法将水平梯度图像稀疏表示和垂直梯度图像稀疏表示进行融合，以将初始重建PET图像从梯度域恢复到图像域，获得重建PET图像。
重建图像判断单元26，用于判断重建PET图像是否满足预设的目标函数，是则，输出该重建PET图像，否则，将该重建PET图像设置为待重建PET图像，并触发初始重建单元22执行通过预设的PET图像重建算法对待重建PET图像进行图像重建步骤。
在本发明实施例中，优选地，目标函数表示为：
Figure PCTCN2019071087-appb-000017
其中，g为投影数据，M为系统矩阵，f为待重建PET图像，v 1为预设大于0的惩罚参数，
Figure PCTCN2019071087-appb-000018
和
Figure PCTCN2019071087-appb-000019
表示水平方向和垂直方向的差分算子，
Figure PCTCN2019071087-appb-000020
表示f的梯度图像，
Figure PCTCN2019071087-appb-000021
和
Figure PCTCN2019071087-appb-000022
分别表示f的水平梯度图像和垂直梯度图像，
Figure PCTCN2019071087-appb-000023
为从
Figure PCTCN2019071087-appb-000024
中提取出的第l个图像块的向量表示，D为预设的过完备字典，α l为第l个图像块所对应的稀疏系数，T 0为每个图像块的稀疏度，通过自适应稀疏变换算法结合迭代重建算法，来实现重建图像对真实图像的不断逼近，从而降低在PET检查中使用的放射性药物的剂量，并提高了PET图像重建的成像效果。
因此，如图3所示，优选地，梯度图像获取单元23包括：
梯度图获取子单元231，用于根据预设的水平梯度图像公式和预设垂直梯度图像公式对初始重建PET图像进行梯度运算，获得初始重建PET图像对应的水平梯度图像和垂直梯度图像，其中，水平梯度图像公式为
Figure PCTCN2019071087-appb-000025
垂直梯度图像公式为
Figure PCTCN2019071087-appb-000026
Figure PCTCN2019071087-appb-000027
为初始重建PET图像，j和k分别为
Figure PCTCN2019071087-appb-000028
中像素的坐标。
字典学习单元24包括：
图像块提取单元241，用于根据预设的图像块数量对水平梯度图像和垂直梯度图像进行图像块提取，得到对应的水平梯度图像块和垂直梯度图像块；以及
字典学习子单元242，用于对水平梯度图像块和垂直梯度图像块进行字典学习，获得对应的水平梯度图像稀疏表示和垂直梯度图像稀疏表示。
在本发明实施例中，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。
实施例三：
图4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4包括处理器40、存储器41以及存储在存储器41中并可在处理器40上运行的计算机程序42。该处理器40执行计算机程序42时实现上述低剂量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S108。或者，处理器40执行计算机程序42时实现上述各装置实施例中各单元的功能，例如图2所示单元21至26的功能。
在本发明实施例中，根据采集到的投影数据和PET设备的系统矩阵，通过PET图像重建算法对待重建PET图像进行重建，获得初始重建PET图像，通过梯度运算和字典学习，分别获得初始重建PET图像对应的水平梯度图像稀疏表示和垂直梯度图像稀疏表示，将水平梯度图像稀疏表示和垂直梯度图像稀疏表示从梯度域恢复到图像域，获得重建PET图像，判断重建PET图像是否满足目标函数，是则输出重建PET图像，否则，继续对待重建PET图像执行图像重建、梯度运算以及字典学习的操作，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4中处理器40执行计算机程序42时实现低剂量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S108。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2所示单元21至26的功能。
在本发明实施例中，根据采集到的投影数据和PET设备的系统矩阵，通过PET图像重建算法对待重建PET图像进行重建，获得初始重建PET图像，通过梯度运算和字典学习，分别获得初始重建PET图像对应的水平梯度图像稀疏表示和垂直梯度图像稀疏表示，将水平梯度图像稀疏表示和垂直梯度图像稀疏表示从梯度域恢复到图像域，获得重建PET图像，判断重建PET图像是否满足目标函数，是则输出重建PET图像，否则，继续对待重建PET图像执行图像重建、梯度运算以及字典学习的操作，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 (10)

  1. 一种低剂量PET图像重建方法，其特征在于，所述方法包括下述步骤：
    当接收到对低剂量PET图像进行重建的请求时，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；
    对所述初始重建PET图像进行梯度运算，获得所述初始重建PET图像对应的水平梯度图像和垂直梯度图像；
    对所述水平梯度图像和所述垂直梯度图像分别进行字典学习，获得对应的水平梯度图像稀疏表示和垂直梯度图像稀疏表示；
    通过最小二乘法将所述水平梯度图像稀疏表示和所述垂直梯度图像稀疏表示从梯度域恢复到图像域，获得重建PET图像；
    判断所述重建PET图像是否满足预设的目标函数，是则，输出所述重建PET图像，否则，将所述重建PET图像设置为所述待重建PET图像，并跳转到通过预设的PET图像重建算法对预先初始化的待重建PET图像进行图像重建的步骤。
  2. 如权利要求1所述的方法，其特征在于，所述目标函数表示为：
    Figure PCTCN2019071087-appb-100001
    其中，g为所述投影数据，M为所述系统矩阵，f为所述待重建PET图像，v 1为预设大于0的惩罚参数，
    Figure PCTCN2019071087-appb-100002
    和
    Figure PCTCN2019071087-appb-100003
    表示水平方向和垂直方向的差分算子，
    Figure PCTCN2019071087-appb-100004
    表示所述f的梯度图像，
    Figure PCTCN2019071087-appb-100005
    和
    Figure PCTCN2019071087-appb-100006
    分别表示所述f的水平梯度图像和垂直梯度图像，
    Figure PCTCN2019071087-appb-100007
    为从所述
    Figure PCTCN2019071087-appb-100008
    中提取出的第l个图像块的向量表示，D为预设的过完备字典，α l为所述第l个图像块所对应的稀疏系数，T 0为所述每个图像块的稀疏度。
  3. 如权利要求1所述的方法，其特征在于，对所述初始重建PET图像进 行梯度运算的步骤，包括：
    根据预设的水平梯度图像公式和预设的垂直梯度图像公式对所述初始重建PET图像进行梯度运算，获得所述初始重建PET图像对应的水平梯度图像和垂直梯度图像，其中，所述水平梯度图像公式为
    Figure PCTCN2019071087-appb-100009
    所述垂直梯度图像公式为
    Figure PCTCN2019071087-appb-100010
    Figure PCTCN2019071087-appb-100011
    为所述初始重建PET图像，j和k分别为所述
    Figure PCTCN2019071087-appb-100012
    中像素的坐标。
  4. 如权利要求1所述的方法，其特征在于，对所述水平梯度图像和所述垂直梯度图像分别进行字典学习的步骤，包括：
    根据预设的图像块数量对所述水平梯度图像和所述垂直梯度图像进行图像块提取，得到对应的水平梯度图像块和垂直梯度图像块；
    对所述水平梯度图像块和所述垂直梯度图像块进行字典学习，获得对应的所述水平梯度图像稀疏表示和所述垂直梯度图像稀疏表示。
  5. 一种低剂量PET图像重建装置，其特征在于，所述装置包括：
    参数获取单元，用于当接收到对低剂量PET图像进行重建的请求时，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；
    梯度图像获取单元，用于对所述初始重建PET图像进行梯度运算，获得所述初始重建PET图像对应的水平梯度图像和垂直梯度图像；
    字典学习单元，用于对所述水平梯度图像和所述垂直梯度图像分别进行字典学习，获得对应的水平梯度图像稀疏表示和垂直梯度图像稀疏表示；
    重建图像获取单元，用于通过最小二乘法将所述水平梯度图像稀疏表示和所述垂直梯度图像稀疏表示从梯度域恢复到图像域，获得重建PET图像；以及
    重建图像判断单元，用于判断所述重建PET图像是否满足预设的目标函数，是则，输出所述重建PET图像，否则，将所述重建PET图像设置为所述待重建 PET图像，并触发所述初始重建单元执行通过预设的PET图像重建算法对预先初始化的待重建PET图像进行图像重建的步骤。
  6. 如权利要求5所述的装置，其特征在于，所述目标函数表示为：
    Figure PCTCN2019071087-appb-100013
    其中，g为所述投影数据，M为所述系统矩阵，f为所述待重建PET图像，v 1为预设大于0的惩罚参数，
    Figure PCTCN2019071087-appb-100014
    和
    Figure PCTCN2019071087-appb-100015
    表示水平方向和垂直方向的差分算子，
    Figure PCTCN2019071087-appb-100016
    表示所述f的梯度图像，
    Figure PCTCN2019071087-appb-100017
    和
    Figure PCTCN2019071087-appb-100018
    分别表示所述f的水平梯度图像和垂直梯度图像，
    Figure PCTCN2019071087-appb-100019
    为从所述
    Figure PCTCN2019071087-appb-100020
    中提取出的第l个图像块的向量表示，D为预设的过完备字典，α l为所述第l个图像块所对应的稀疏系数，T 0为所述每个图像块的稀疏度。
  7. 如权利要求5所述的装置，其特征在于，所述梯度图像获取单元包括：
    梯度图获取子单元，用于根据预设的水平梯度图像公式和预设的垂直梯度图像公式对所述初始重建PET图像进行梯度运算，获得所述初始重建PET图像对应的水平梯度图像和垂直梯度图像，其中，所述水平梯度图像公式为
    Figure PCTCN2019071087-appb-100021
    所述垂直梯度图像公式为
    Figure PCTCN2019071087-appb-100022
    Figure PCTCN2019071087-appb-100023
    为所述初始重建PET图像，j和k分别为所述
    Figure PCTCN2019071087-appb-100024
    中像素的坐标。
  8. 如权利要求5所述的装置，其特征在于，所述字典学习单元包括：
    图像块提取单元，用于根据预设的图像块数量对所述水平梯度图像和所述垂直梯度图像进行图像块提取，得到对应的水平梯度图像块和垂直梯度图像块；以及
    字典学习子单元，用于对所述水平梯度图像块和所述垂直梯度图像块进行字典学习，获得对应的所述水平梯度图像稀疏表示和所述垂直梯度图像稀疏表示。
  9. 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4任一项所述方法的步骤。
  10. 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4任一项所述方法的步骤。
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