基于无偏线性最优估计的PET图像重建

doi:10.11896/jsjkx.181202329

摘要/Abstract

摘要： 正电子发射断层成像(Positron Emission Tomography,PET)技术在实体肿瘤的定性诊断和病灶转移的检查中具有举足轻重的作用,因此非常有必要提高PET的成像质量。然而,已有的迭代重建算法基本上都严重依赖于PET的线性模型。考虑到探测器效率、探测系统的几何尺寸、生物组织对光子的衰减以及散射效应等诸多物理因素,该模型无法真实地刻画示踪剂与正弦图数据之间的复杂关系。文中首先提出了一种新的观测模型,通过在原来的线性模型中引入未知输入项来刻画示踪剂与正弦图数据之间的关系。该项由两部分组成:1)系数矩阵,用于进一步描述投影的线性部分;2)未知输入,用于刻画示踪剂的浓度分布和投影数据之间的一些非线性关系。在此新模型的基础上,PET图像重构问题被转化成一个线性无偏的最优估计问题。然后,给出了具有待定增益的线性迭代估计模型,通过将正弦数据向未知输入项的系数矩阵的零空间零域上进行投影,消除了未知输入给线性最优估计带来的困难,借助卡尔曼滤波的设计思路,推导出了前述的估计增益。基于此估计模型,提出了一种基于无偏线性最优估计的重建算法。最后,通过仿真实验,将所提重建算法与期望极大估计算法(Expectation-Maximization reconstruction,EM)、核化的EM算法(Kernel method,KEM)以及基于标准卡尔曼滤波(Kalman Filtering method,KF)的重建算法从均方误差(Mean Square Error,MSE)、信噪比(Signal-Noise-Rate,SNR)两个方面进行了比较。实验结果表明:与其他3种算法相比,所提算法重建的图像具有更大的信噪比、更小的均方误差,视觉上更加清晰,更好地重建了肿瘤的形状和尺寸,因此具有更好的重构质量。

关键词: 卡尔曼滤波, 未知输入, 无偏估计, 最优估计

Abstract: Positron Emission Tomography (PET) plays an important role in qualitative diagnosis and metastasis of tumors.Therefore,it is very necessary to improve imaging quality of PET.However,most of the existing reconstruction algorithms rely heavily on the linear model of PET.Considering that PET is affected by many physical factors,such as detector efficiency,geometric size of detection system,attenuation of gamma photons by biological tissues and scattering effects,the linear model cannot match the nonlinear relationship between tracer concentration and sinogram.This paper proposed a new observation model to characterize the complicated relationship between the tracer concentration and sinogram by introducing an unknown input term.This term consists of two parts.One is a coefficient matrix,which further describes the linear part of the projection; the other is an unknown input,which characterizes the nonlinear relation ship between the tracer concentration and the sinogram.Based on the new model,the PET image reconstruction is reformulated as a linear unbiased optimal estimation.Then,a linear and recursive relation with an unknown estimation gain is introduced,the difficulty induced by the unknown input term is solved by projecting sinogram onto the null space of the coefficient matrix of unknown input.Based on the design idea of Kalman filter,the estimation gain is derived.Finally,the Expectation-Maximization reconstruction (EM),the Kernel-based EM algorithm (KEM) and the Kalman Filtering method (KF) are compared with the proposed algorithm by calculating Mean Square Error (MSE) and Signal-Noise-Rate (SNR).The experiment results show that the proposed algorithm has larger SNR,smaller MSE as well as more clear reconstruct image,and reconstructs the size and shape of the tumor better than the others.Hence,the proposed algorithm of reconstruction has better quality to the others.

Key words: Kalman filter, Optimal estimation, Unbiased estimation, Unknown input

中图分类号:

TP13

王宏霞,徐英婕,赵云波,张文安. 基于无偏线性最优估计的PET图像重建[J]. 计算机科学, 2020, 47(1): 165-169. https://doi.org/10.11896/jsjkx.181202329

WANG Hong-xia,XU Ying-jie,ZHAO Yun-bo,ZHANG Wen-an. PET Image Reconstruction Based on Unbiased Linear Optimal Estimation[J]. Computer Science, 2020, 47(1): 165-169. https://doi.org/10.11896/jsjkx.181202329

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