WO2021232653A1 - 一种结合滤波反投影算法和神经网络的pet图像重建算法 - Google Patents

一种结合滤波反投影算法和神经网络的pet图像重建算法 Download PDF

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WO2021232653A1
WO2021232653A1 PCT/CN2020/117949 CN2020117949W WO2021232653A1 WO 2021232653 A1 WO2021232653 A1 WO 2021232653A1 CN 2020117949 W CN2020117949 W CN 2020117949W WO 2021232653 A1 WO2021232653 A1 WO 2021232653A1
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pet
fbp
net
reconstruction
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刘华锋
王博
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浙江大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—2D [Two Dimensional] image generation
    • G06T11/003—Reconstruction from projections, e.g. tomography
    • G06T11/005—Specific pre-processing for tomographic reconstruction, e.g. calibration, source positioning, rebinning, scatter correction, retrospective gating
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/045—Combinations of networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/70—Denoising; Smoothing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10072—Tomographic images
    • G06T2207/10104—Positron emission tomography [PET]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20024—Filtering details

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  • the invention belongs to the technical field of biomedical image analysis, and specifically relates to a PET image reconstruction algorithm combining a filtered back projection algorithm and a neural network.
  • PET Positron Emission Tomography
  • the radionuclide decays in the organism to produce positrons, which collide with free electrons and annihilate, producing a pair of gamma photons with an energy of 511KeV and flying in opposite directions.
  • the surrounding detector array of PET performs coincidence measurement and counting of gamma photon pairs to obtain the original projection data (sinogram), which provides data support for post-image reconstruction and analysis.
  • PET images provide doctors with visual and intuitive information for diagnosing patients.
  • PET reconstruction algorithms can be divided into three categories: analytical reconstruction algorithms, iterative reconstruction algorithms and deep learning reconstruction methods.
  • Analytical reconstruction algorithms such as the filtered back-projection (FBP) algorithm, are based on the central slice theorem, and the sinogram is first filtered in the frequency domain and then back-projected. This type of method has the advantages of being simple and fast, but the reconstructed image obtained contains a lot of noise and wheel-shaped artifacts.
  • FBP filtered back-projection
  • the iterative reconstruction algorithm uses Poisson or Gaussian models to describe the noise and establish the reconstruction objective function.
  • this type of method often adds a priori constraint to the objective function, such as Markov random field, TV, etc.
  • a priori constraint such as Markov random field, TV, etc.
  • the iterative reconstruction algorithm uses a noise model, which suppresses the noise in the reconstruction image to a certain extent.
  • it has a large amount of calculation and a slow speed, and the choice of a priori form and hyperparameters relies on experience, so there is no uniform standard for the time being.
  • the present invention proposes a PET image reconstruction algorithm that combines a filtered back-projection algorithm and a neural network.
  • the reconstruction problem is split into two sub-problems, reconstruction and denoising, and a filtered back-projection layer is used respectively.
  • improved denoising convolutional neural network to solve.
  • a PET image reconstruction algorithm combining a filtered back projection algorithm and a neural network, including the following steps:
  • Step 1 Inject a PET radiotracer into the biological tissue, scan it with PET equipment, detect and count the coincident photons, and obtain the original projection data matrix Y;
  • Step 2 Establish a measurement equation model according to the principle of PET imaging
  • G is the system matrix
  • X is the true tracer concentration distribution map
  • R is the random photon number during the measurement process
  • S is the scattered photon number during the measurement process
  • Step 3 Split the reconstruction problem into two sub-problems
  • the first sub-problem is the reconstruction problem
  • the initial reconstruction image F 1 (Y) containing noise is obtained from the original projection data matrix Y
  • the second sub-problem is the denoising problem, removing the noise F 2 (R in F 1 (Y) +S), get the PET reconstructed image X;
  • Step 4 The first sub-problem is solved by the filtered back projection (FBP) layer, and the second sub-problem is solved by the improved denoising convolutional neural network (DnCNN).
  • the filtered back projection layer and the improved denoising convolutional neural network are connected in series to form a filter Back projection network, namely FBP-Net;
  • Step 5 input the original projection data (sinogram) into FBP-Net, use the image obtained by the traditional reconstruction algorithm as the label, adjust the parameters of FBP-Net, and reduce the error between the FBP-Net output and the label;
  • Step 6 input the projection data to be reconstructed into the trained FBP-Net to directly obtain the required reconstruction image.
  • the PET scanning mode in step 1 is static scanning or dynamic scanning.
  • the filtering back projection layer in step 4 inputs PET projection data, and outputs a preliminary reconstructed image of PET containing noise.
  • the filtering back projection layer is based on filtering back projection algorithms, including frequency domain filtering and back projection; among them, the back projection method uses traditional filtering back projection algorithms, the filters used in frequency domain filtering are learnable, and each The angle projection data corresponds to an independent one-dimensional frequency domain filter.
  • the improved denoising convolutional neural network in step 4 removes the noise in the reconstructed image through residual learning.
  • the improved denoising convolutional neural network contains 8 2D convolutional layers and a normalization layer, each convolutional layer contains 64 3 ⁇ 3 filters, and the first 7 convolutional layers use activation functions ReLU and batch normalized BN; 8 convolutional layers learn the residuals between the noisy reconstructed image and the clean reconstructed image; the input of the denoising network is subtracted from the output of the 8th convolutional layer, and then normalized Layer to obtain a clean reconstruction map.
  • step 5 both the original projection data (sinogram) and the label need to be normalized for a single frame
  • X min and X max are the minimum and maximum values of a single frame of data, respectively.
  • step 5 is as follows:
  • Step 5.1 initialize the parameters of FBP-Net, initialize all frequency domain filters of the FBP layer with a ramp filter, and initialize the parameters in the improved DnCNN with a truncated normal distribution;
  • Step 5.2 input the sinogram of the training set into FBP-Net, calculate the output of each layer through the forward propagation formula, and then obtain the final output of FBP-Net;
  • Step 5.3 calculate the loss function between the output of FBP-Net and the label
  • I the estimated value of the i-th sample output by FBP-Net
  • X(i) is the label of the i-th sample
  • Step 5.4 find the partial derivative of the loss function, and update the learnable parameters in FBP-Net through the Adam algorithm;
  • Step 5.5 repeat steps (5-2) to (5-4) until the value change of the loss function is less than 10 -5 . Further, in step 6, normalization processing is performed before inputting the projection data to be reconstructed into the trained FBP-Net.
  • the input of FBP-Net is 2D PET scan data.
  • the beneficial effects of the present invention are: combining the traditional filtering back-projection algorithm and neural network, an interpretable deep neural network structure is proposed for PET image reconstruction.
  • the reconstruction problem is divided into two sub-problems, reconstruction and denoising, which are solved by using a filtered back projection layer and an improved denoising convolutional neural network respectively.
  • the filtering back-projection layer regards the frequency domain filter as learnable, and reconstructs the reconstructed image with noise from the sinogram; the improved DnCNN removes the noise in the reconstructed image, thereby obtaining a clear reconstructed image.
  • the present invention solves the problem that deep learning is difficult to explain when used in image reconstruction, and can still reconstruct a clear PET image under the condition of low count rate.
  • Figure 1 is a flow chart of the implementation of the present invention
  • Figure 2 is a schematic diagram of the structure of FBP-Net proposed by the present invention.
  • Figure 3 is a comparison of 18 F-FDG reconstruction images of different methods at different count rates; among them, the first column is the reconstruction image obtained by the present invention, the second column is the reconstruction image of the MLEM algorithm, and the third column is the TV algorithm In the reconstructed image, the fourth column is the true value, and the A row, the B row, and the C row correspond to counting rates of 1 ⁇ 10 5 , 5 ⁇ 10 5 , and 1 ⁇ 10 6, respectively .
  • the present invention combines the filtering back-projection algorithm and the PET image reconstruction algorithm of the neural network.
  • the overall implementation flow chart is shown in Fig. 1, which specifically includes the following steps:
  • G is the system matrix
  • X is the true tracer concentration distribution map
  • R is the random photon number during the measurement process
  • S is the scattered photon number during the measurement process.
  • the first sub-problem is the reconstruction problem.
  • the original projection data matrix Y is reconstructed to obtain a preliminary reconstruction image F 1 (Y).
  • the preliminary reconstruction image F 1 (Y) contains a lot of noise. Since the raw PET detection data contains scattering coincidence events and random coincidence events, the number of true coincidence events that can be used for reconstruction is less than half of the total detection events. If no scatter correction is performed With random correction, the reconstructed image will be affected by random photons and scattered photons, and the contrast and details of the image will not be good enough.
  • the noise here means that when random correction and scattering correction are not performed, random photons and scattered photons lead to reconstruction. The quality of the picture has deteriorated.
  • the second sub-problem is the denoising problem.
  • the noise F 2 (R+S) in F 1 (Y) is removed, and the PET reconstructed image X is obtained.
  • the PET reconstructed image X removes the influence of scattered photons and random photons on the reconstructed image, and removes the artifacts that may exist in the preliminary reconstruction image F 1 (Y) obtained in the previous step, to obtain high contrast, clear details, and no artifacts
  • the reconstructed PET image X is a high-quality PET reconstructed image X.
  • the first sub-problem is solved by a filtered back projection layer
  • the second sub-problem is solved by an improved denoising convolutional neural network.
  • the filtered back projection layer and the improved denoising convolutional neural network are connected in series to form a filtered back projection network, namely FBP-Net.
  • the filtering back projection layer inputs the PET projection data, and outputs the preliminary reconstructed image of the PET with noise.
  • the filtering back-projection layer is based on filtering back-projection algorithms, including frequency-domain filtering and back-projection; among them, the method of back-projection is the same as the traditional filtering back-projection algorithm.
  • the filters used in frequency-domain filtering are learnable, and each angle
  • the projection data corresponds to an independent one-dimensional frequency domain filter.
  • the improved denoising convolutional neural network uses residual learning to remove the noise in the reconstructed image.
  • the improved denoising convolutional neural network contains 8 2D convolutional layers and a normalization layer.
  • Each convolutional layer contains 64 3 ⁇ 3 filters, and the first 7 convolutional layers use the activation function ReLU and batch Normalized BN; 8 convolutional layers learn the residuals between the noisy reconstructed image and the clean reconstructed image; the input of the denoising network is subtracted from the output of the 8th convolutional layer, and then the normalized layer is used to obtain A clean reconstructed image, that is, a PET reconstructed image with noise removed.
  • the traditional reconstruction algorithm is used to reconstruct the image from the sinogram as the label, and the sinogram and the label are normalized in a single frame.
  • the normalization formula is as follows,
  • X min and X max are the minimum and maximum values of a single frame of data, respectively.
  • the frequency domain filter of the FBP layer is initialized with the ramp filter, and the parameters in the improved DnCNN are initialized with the truncated normal distribution.
  • Input the sinogram of the training set into FBP-Net calculate the output of each layer through the forward propagation formula, and then obtain the final output of FBP-Net. Calculate the loss function between the output of FBP-Net and the label,
  • the simulated tracer is 18 F-FDG
  • the phantom is the chest cavity
  • the simulated scanner is Siemens Biograph PET/CT.
  • the simulated scan time is 40 minutes
  • the time frame is 18 frames
  • three count rates are considered, 1 ⁇ 10 5 , 5 ⁇ 10 5 , and 1 ⁇ 10 6
  • 30 sets of dynamic PET data are simulated for each count rate.
  • the simulation data of these three count rates are randomly divided into training set (1134 sinograms) and test set (486 sinograms).
  • the training set is used to learn the parameters of FBP-Net
  • the test set is used to test the performance of the trained FBP-Net.
  • Figure 3 compares the reconstruction diagrams of the present invention and the traditional reconstruction method at three count rates.
  • the first column is the reconstruction image obtained by the present invention
  • the second column is the reconstruction image of the MLEM algorithm
  • the third column is the reconstruction image of the TV algorithm
  • the fourth column is the true value.
  • Rows A, B, and C correspond to The counting rate is 1 ⁇ 10 5 , 5 ⁇ 10 5 , 1 ⁇ 10 6 .
  • the reconstructed image of the present invention has rich details and low noise, and is closest to the true value image; the reconstructed image of the MLEM algorithm contains a lot of noise; the reconstructed image of the TV is too smooth, and some details are lost.
  • the reconstructed image of the present invention is almost unaffected and is still very close to the true value image; the noise in the MLEM reconstruction image becomes larger and larger; the detail loss of the TV reconstruction image becomes more and more serious, and even appears Uneven small pieces. It can be seen that the method proposed by the present invention can obtain high-quality PET reconstruction images, and is not sensitive to the count rate, and can still reconstruct high-quality images even under the condition of a low count rate.
  • the input of FBP-Net is 2D PET scan data. If the original collected data is in 3D form, it needs to be converted into 2D scan data through methods such as SSRB and FORB.
  • the present invention combines the traditional filtering back-projection algorithm and neural network, and proposes an interpretable deep neural network structure for PET image reconstruction.
  • the reconstruction problem is divided into two sub-problems, reconstruction and denoising, which are solved by using a filtered back projection layer and an improved denoising convolutional neural network respectively.
  • the filtering back-projection layer regards the frequency domain filter as learnable, and reconstructs the reconstructed image with noise from the sinogram; the improved DnCNN removes the noise in the reconstructed image, thereby obtaining a clear reconstructed image.
  • the present invention solves the problem that deep learning is difficult to explain when used in image reconstruction, and can still reconstruct a clear PET image under the condition of low count rate.

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Abstract

一种结合滤波反投影算法和神经网络的PET图像重建算法，包括如下步骤：步骤1，给生物组织注入PET放射性示踪剂，用PET设备进行扫描，探测符合光子并进行计数，得到原始投影数据矩阵Y；步骤2，根据PET成像原理，建立测量方程模型；步骤3，将重建问题拆分成重建和去噪两个子问题；步骤4，重建子问题采用滤波反投影(FBP)层解决，去噪子问题采用改进的去噪卷积神经网络(DnCNN)解决；步骤5，在训练阶段，调整FBP-Net的参数，降低FBP-Net输出和标签之间的误差；步骤6，在估计阶段，把待重建的投影数据输入训练好的FBP-Net，直接获得所需的重建图。该方法解决了深度学习用于图像重建时难以解释的问题，在低计数率的情况下，依然能够重建清楚的PET图像。

Description

一种结合滤波反投影算法和神经网络的PET图像重建算法 技术领域
本发明属于生物医学图像分析技术领域，具体涉及一种结合滤波反投影算法和神经网络的PET图像重建算法。
背景技术
正电子发射断层扫描(Positron Emission Tomography，PET)是一种用于活体功能显像的核医学技术，能够在分子水平上提供脏器及病变的功能信息，在心脏疾病、脑疾病和恶性肿瘤的诊断和治疗方面发挥着不可替代的作用。PET使用 15O， 18F等放射性核素标记的葡萄糖、蛋白质等物质作为示踪剂，这些示踪剂都是生物体的重要组成成分，正常参与生物体的代谢活动，不会对生物体造成伤害。放射性核素在生物体内发生衰变产生正电子，与自由电子碰撞湮灭，产生一对能量为511KeV、沿相反方向飞出的γ光子。PET的环绕型探测器阵列对γ光子对进行符合测量和计数，得到原始的投影数据(sinogram)，为后期图像重建和分析提供数据支撑。
PET图像为医生诊断病人提供了形象直观的信息，但是受到低分辨率、计数率不高、噪声大等因素的影响，快速获得高质量的重建图一直是PET成像领域的重要研究课题。PET重建算法可以分为三类：解析重建算法、迭代重建算法和深度学习重建方法。解析重建算法，如滤波反投影(Filtered back-projection，FBP)算法，基于中心切片定理，先对sinogram进行频域滤波，然后进行反投影。该类方法具有简单快速的优点，但是获得的重建图含有大量噪声和车轮状伪影。迭代重建算法采用泊松或高斯模型来描述噪声，建立重建的目标函数。为了抑制重建图像的噪声，该类方法常常在目标函数中加入先验约束，例如马尔科夫随机场、TV等。先验形式的种类繁多，难以判断何种先验形式是最优的。相比于解析重建算法，迭代重建算法使用了噪声模型，在一定程度上抑制了重建图中的噪声。但是，它的计算量大速度慢，而且先验形式和超参数的选择依 靠经验，暂无统一标准。
近年来，很多学者利用深度神经网络进行PET图像重建。他们使用相对成熟的深度神经网络结构，如U-net、生成对抗网络(GAN)、编码-解码结构等，向神经网络输入sinogram或者传统方法得到的低质量重建图，通过监督学习，使神经网络输出高质量的重建图。尽管这些方法在重建问题上取得了一定成绩，但是这些方法使用的网络像黑箱，难以解释。此外，为了取得较好的结果，这些方法往往需要大量高质量的数据来训练，而数据是医学图像领域的稀缺资源。开发可解释的神经网络来解决PET图像重建问题，降低对数据量的要求，是一个值得研究的方向。
发明内容
针对现有技术所存在的上述问题，本发明提出了一种结合滤波反投影算法和神经网络的PET图像重建算法，将重建问题拆分成重建和去噪两个子问题，分别用滤波反投影层和改进的去噪卷积神经网络解决。
为实现上述目的，本发明采用如下技术方案：一种结合滤波反投影算法和神经网络的PET图像重建算法，包括如下步骤：
步骤1，给生物组织注入PET放射性示踪剂，用PET设备进行扫描，探测符合光子并进行计数，得到原始投影数据矩阵Y；
步骤2，根据PET成像原理，建立测量方程模型，
Y＝GX+R+S  (1)
其中，G为***矩阵，X是真实的示踪剂浓度分布图，R为测量过程中的随机光子数，S为测量过程中的散射光子数；
步骤3，将重建问题拆分成两个子问题，
X＝F 1(Y)-F 2(R+S)  (2)
其中，子问题一是重建问题，由原始投影数据矩阵Y重建得到含有噪声的初步重建图F 1(Y)，子问题二是去噪问题，去除F 1(Y)中的噪声F 2(R+S)，得到PET重建图像X；
步骤4，子问题一采用滤波反投影(FBP)层解决，子问题二采用改进的去噪卷积神经网络(DnCNN)解决，滤波反投影层和改进的去噪卷积神经网络串 联，组成滤波反投影网络，即FBP-Net；
步骤5，在训练阶段，把原始投影数据(sinogram)输入FBP-Net，将传统重建算法获得的图像作为标签，调整FBP-Net的参数，降低FBP-Net输出和标签之间的误差；
步骤6，在估计阶段，把待重建的投影数据输入训练好的FBP-Net，直接获得所需的重建图。
进一步地，步骤1中的PET扫描方式为静态扫描或者动态扫描。
进一步地，步骤4中的滤波反投影层输入PET投影数据，输出含有噪声的PET初步重建图。
进一步地，滤波反投影层基于滤波反投影算法，包括频域滤波和反投影；其中，反投影的做法采用传统的滤波反投影算法，频域滤波使用的滤波器是可学习的，并且每个角度的投影数据对应一个独立的一维频域滤波器。
进一步地，步骤4中改进的去噪卷积神经网络通过残差学习，去除重建图中的噪声。
进一步地，改进的去噪卷积神经网络包含8个2D卷积层和一个归一化层，每个卷积层包含64个3×3的滤波器，并且前7个卷积层使用激活函数ReLU和批归一化BN；8个卷积层学习含有噪声的重建图和干净重建图之间的残差；去噪网络的输入减去第8个卷积层的输出，然后通过归一化层，获得干净的重建图。
进一步地，步骤5中原始投影数据(sinogram)和标签均需要进行单帧的归一化，
Figure PCTCN2020117949-appb-000001
其中，X min和X max分别是单帧数据的最小值和最大值。
进一步地，步骤5的具体过程如下：
步骤5.1，初始化FBP-Net的参数，用ramp滤波器初始化FBP层的所有频域滤波器，用截断正态分布初始化改进的DnCNN中的参数；
步骤5.2，将训练集的sinogram输入FBP-Net，通过正向传播公式计算每层的输出，进而获得FBP-Net最终的输出；
步骤5.3，计算FBP-Net的输出和标签之间的损失函数，
Figure PCTCN2020117949-appb-000002
其中，
Figure PCTCN2020117949-appb-000003
是FBP-Net输出的第i个样本的估计值，X(i)是第i个样本的标签；
步骤5.4，求损失函数的偏导数，通过Adam算法更新FBP-Net中可学习的参数；
步骤5.5，重复执行步骤(5-2)到(5-4)，直到损失函数的数值变化小于10 -5。进一步地，步骤6中把待重建的投影数据输入训练好的FBP-Net之前进行归一化处理。
进一步地，FBP-Net的输入是2D的PET扫描数据。
本发明的有益效果在于：结合了传统的滤波反投影算法和神经网络，提出了一种可解释的深度神经网络结构，用于PET图像重建。将重建问题拆分为重建和去噪两个子问题，分别使用滤波反投影层和改进的去噪卷积神经网络解决。滤波反投影层将频域滤波器看作可学习的，由sinogram重建含有噪声的重建图；改进的DnCNN去除重建图像中的噪声，从而获得清楚的重建图。本发明解决了深度学习用于图像重建时难以解释的问题，在低计数率的情况下，依然能够重建清楚的PET图像。
附图说明
图1为本发明的实施流程图；
图2为本发明提出的FBP-Net的结构示意图；
图3为不同方法在不同计数率下的 18F-FDG重建图的对比；其中，第1列为本发明获得的重建图，第2列为MLEM算法的重建图，第3列为TV算法的重建图，第4列为真值，A行、B行、C行分别对应计数率1×10 5、5×10 5、1×10 6。
具体实施方式
为了更为具体地描述本发明，下面结合附图及具体实施方式对本发明的技术方案进行详细说明。
本发明结合滤波反投影算法和神经网络的PET图像重建算法，整体实施流 程图如图1所示，具体包括如下步骤：
(1)采集数据。给研究对象注射适量PET放射性示踪剂，用PET设备进行静态或动态扫描，探测符合光子并进行计数，得到原始投影数据矩阵Y。
(2)分解重建问题，确定神经网络的结构如图2。
根据PET成像原理，建立测量方程模型，
Y＝GX+R+S  (1)
其中：G为***矩阵，X是真实的示踪剂浓度分布图，R为测量过程中的随机光子数，S为测量过程中的散射光子数。
对测量方程模型进行变换，将重建问题拆分成两个子问题，
X＝F 1(Y)-F 2(R+S)  (2)
子问题一是重建问题，由原始投影数据矩阵Y重建得到初步重建图F 1(Y)。该初步重建图F 1(Y)含有大量噪声，由于PET原始探测数据中含有散射符合事件和随机符合事件，可用于重建的真符合事件的数量不及总探测事件数的一半，如果不进行散射矫正和随机矫正，重建图就会受到随机光子和散射光子的影响，图像的对比度和细节就会不够好，此处的噪声指的就是未进行随机矫正和散射矫正时，随机光子和散射光子导致重建图的质量变差。子问题二是去噪问题，去除F 1(Y)中的噪声F 2(R+S)，得到PET重建图像X。该PET重建图像X去除了散射光子和随机光子对重建图的影响，以及去除上一步获得的初步重建图F 1(Y)中可能存在的伪影，获得对比度高、细节清楚、不含有伪影的重建图，该PET重建图像X是高质量的PET重建图像X。
子问题一采用滤波反投影层解决，子问题二采用改进的去噪卷积神经网络解决。滤波反投影层和改进的去噪卷积神经网络串联，组成滤波反投影网络，即FBP-Net。
其中，滤波反投影层输入PET投影数据，输出含有噪声的PET初步重建图。滤波反投影层基于滤波反投影算法，包括频域滤波和反投影；其中，反投影的做法和传统的滤波反投影算法一样，频域滤波使用的滤波器是可学习的，并且每个角度的投影数据对应一个独立的一维频域滤波器。改进的去噪卷积神经网络通过残差学习，去除重建图中的噪声。改进的去噪卷积神经网络包含8个2D卷积层和一个归一化层，每个卷积层包含64个3×3的滤波器，并且前7个卷 积层使用激活函数ReLU和批归一化BN；8个卷积层学习含有噪声的重建图和干净重建图之间的残差；去噪网络的输入减去第8个卷积层的输出，然后通过归一化层，获得干净的重建图，即去除噪声的PET重建图像。
(3)训练阶段。
采用传统重建算法由sinogram重建获得图像作为标签，对sinogram和标签进行单帧归一化。归一化公式如下，
Figure PCTCN2020117949-appb-000004
其中，X min和X max分别是单帧数据的最小值和最大值。
初始化FBP-Net的参数。用ramp滤波器初始化FBP层的频域滤波器，用截断正态分布初始化改进的DnCNN中的参数。将训练集的sinogram输入FBP-Net，通过正向传播公式计算每层的输出，进而获得FBP-Net最终的输出。计算FBP-Net的输出和标签之间的损失函数，
Figure PCTCN2020117949-appb-000005
其中，
Figure PCTCN2020117949-appb-000006
是FBP-Net输出的第i个样本的估计值，X(i)是第i个样本的标签。求损失函数的偏导数，通过Adam算法更新FBP-Net中可学习的参数。重复进行正向传播和反向求导，不断更新FBP-Net的参数，直到损失函数的数值变化足够小，趋于稳定，即使FBP-Net输出和标签之间的误差尽可能小。这是因为在训练开始的时候，损失函数loss的数值下降很快，但是迭代到一定次数之后，loss会下降很慢，并逐渐趋于稳定。此时如果继续训练，时间成本会增多，获得的提升很小。所以在损失函数的数值变化足够小，即loss下降很慢的时候选择结束训练。在本实施例中，当损失函数的数值变化小于10 -5时，选择接受训练。
(4)估计阶段。
先对待重建的sinogram进行归一化，然后将其输入训练好的FBP-Net，直接获得所需的重建图，该重建图去除了散射光子和随机光子对重建图的影响，以及去除了初步重建图中可能存在的伪影，为对比度高、细节清楚、不含有伪影的高质量的重建图。
以下基于蒙特卡洛仿真数据进行实验，以验证本实施方式的有效性。本实 验在一台***是Ubuntu 18.04 LTS的服务器上运行，内存128G，深度学习框架为tensorow 1.13.1，一张NVIDIA TITAN RTX 24GB显卡用于加速代码运行。
仿真的示踪剂是 18F-FDG，体模为胸腔，模拟的扫描仪是西门子Biograph PET/CT。模拟的扫描时间为40min，时间帧为18帧，考虑了三种计数率，1×10 5，5×10 5，1×10 6，对每种计数率仿真了30组动态PET数据。这三种计数率的仿真数据被随机分为训练集(1134 sinograms)和测试集(486 sinograms)。训练集用于学习FBP-Net的参数，测试集用于检验训练好的FBP-Net的性能。
图3比较了本发明和传统重建方法在三种计数率下的重建图。其中，第1列为本发明获得的重建图，第2列为MLEM算法的重建图，第3列为TV算法的重建图，第4列为真值，A行、B行、C行分别对应计数率1×10 5、5×10 5、1×10 6。本发明的重建图细节丰富且噪声低，最接近真值图；MLEM算法的重建图含有很多噪声；TV的重建图过平滑，损失了一部分细节。当计数率从高变低时，本发明的重建图几乎不受影响，依然很接近真值图；MLEM重建图中的噪声越来越大；TV重建图的细节损失越来越严重，甚至出现了不均匀的小块。由此可见，本发明提出的方法能够获得高质量的PET重建图，而且对计数率不敏感，即使在低计数率的条件下，依然能够重建高质量的图像。
在本实施例中，FBP-Net的输入是2D的PET扫描数据，如果原始的采集数据是3D形式，需要通过SSRB、FORB等方法，转化为2D的扫描数据。
本发明结合了传统的滤波反投影算法和神经网络，提出了一种可解释的深度神经网络结构，用于PET图像重建。将重建问题拆分为重建和去噪两个子问题，分别使用滤波反投影层和改进的去噪卷积神经网络解决。滤波反投影层将频域滤波器看作可学习的，由sinogram重建含有噪声的重建图；改进的DnCNN去除重建图像中的噪声，从而获得清楚的重建图。本发明解决了深度学习用于图像重建时难以解释的问题，在低计数率的情况下，依然能够重建清楚的PET图像。
上述对实施例的描述是为便于本技术领域的普通技术人员能理解和应用本发明。熟悉本领域技术的人员显然可以容易地对上述实施例做出各种修改，并把在此说明的一般原理应用到其他实施例中而不必经过创造性的劳动。因此，本发明不限于上述实施例，本领域技术人员根据本发明的揭示，对于本发明做 出的改进和修改都应该在本发明的保护范围之内。

Claims (10)

  1. 一种结合滤波反投影算法和神经网络的PET图像重建算法，包括如下步骤：
    步骤1，给生物组织注入PET放射性示踪剂，用PET设备进行扫描，探测符合光子并进行计数，得到原始投影数据矩阵Y；
    步骤2，根据PET成像原理，建立测量方程模型，
    Y＝GX+R+S  (1)
    其中，G为***矩阵，X是真实的示踪剂浓度分布图，R为测量过程中的随机光子数，S为测量过程中的散射光子数；
    步骤3，将重建问题拆分成两个子问题，
    X＝F 1(Y)-F 2(R+S)  (2)
    其中，子问题一是重建问题，由原始投影数据矩阵Y重建得到含有噪声的初步重建图F 1(Y)，子问题二是去噪问题，去除F 1(Y)中的噪声F 2(R+S)，得到PET重建图像X；
    步骤4，子问题一采用滤波反投影(FBP)层解决，子问题二采用改进的去噪卷积神经网络(DnCNN)解决，滤波反投影层和改进的去噪卷积神经网络串联，组成滤波反投影网络，即FBP-Net；
    步骤5，在训练阶段，把原始投影数据(sinogram)输入FBP-Net，将传统重建算法获得的图像作为标签，调整FBP-Net的参数，降低FBP-Net输出和标签之间的误差；
    步骤6，在估计阶段，把待重建的投影数据输入训练好的FBP-Net，直接获得所需的重建图。
  2. 根据权利要求1所述的PET图像重建算法，其特征在于：步骤1中的PET扫描方式为静态扫描或者动态扫描。
  3. 根据权利要求1所述的PET图像重建算法，其特征在于：步骤4中的滤波反投影层输入PET投影数据，输出含有噪声的PET初步重建图。
  4. 根据权利要求3所述的PET图像重建算法，其特征在于：滤波反投影层基于滤波反投影算法，包括频域滤波和反投影；其中，反投影的做法采用传统 的滤波反投影算法，频域滤波使用的滤波器是可学习的，并且每个角度的投影数据对应一个独立的一维频域滤波器。
  5. 根据权利要求1所述的PET图像重建算法，其特征在于：步骤4中改进的去噪卷积神经网络通过残差学习，去除重建图中的噪声。
  6. 根据权利要求5所述的PET图像重建算法，其特征在于：改进的去噪卷积神经网络包含8个2D卷积层和一个归一化层，每个卷积层包含64个3×3的滤波器，并且前7个卷积层使用激活函数ReLU和批归一化BN；8个卷积层学习含有噪声的重建图和干净重建图之间的残差；去噪网络的输入减去第8个卷积层的输出，然后通过归一化层，获得干净的重建图。
  7. 根据权利要求1所述的PET图像重建算法，其特征在于：步骤5中原始投影数据(sinogram)和标签均需要进行单帧的归一化，
    Figure PCTCN2020117949-appb-100001
    其中，X min和X max分别是单帧数据的最小值和最大值。
  8. 根据权利要求1所述的PET图像重建算法，其特征在于：步骤5的具体过程如下：
    步骤5.1，初始化FBP-Net的参数，用ramp滤波器初始化FBP层的所有频域滤波器，用截断正态分布初始化改进的DnCNN中的参数；
    步骤5.2，将训练集的sinogram输入FBP-Net，通过正向传播公式计算每层的输出，进而获得FBP-Net最终的输出；
    步骤5.3，计算FBP-Net的输出和标签之间的损失函数，
    Figure PCTCN2020117949-appb-100002
    其中，
    Figure PCTCN2020117949-appb-100003
    是FBP-Net输出的第i个样本的估计值，X(i)是第i个样本的标签；
    步骤5.4，求损失函数的偏导数，通过Adam算法更新FBP-Net中可学习的参数；
    步骤5.5，重复执行步骤(5-2)到(5-4)，直到损失函数的数值变化小于10 -5。
  9. 根据权利要求1所述的PET图像重建算法，其特征在于：步骤6中把待重建的投影数据输入训练好的FBP-Net之前进行归一化处理。
  10. 根据权利要求1至9任一项所述的PET图像重建算法，其特征在于： FBP-Net的输入是2D的PET扫描数据。
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