基于最大期望算法的电阻抗成像系统的图像重建

The Images Reconstruction of Electrical Impedance Tomography by EM Method

电阻抗成像EIT(Electrical impedance tomography)技术利用不同媒质具有不同的电导率这一物理基础,通过测量目标场在一定电刺激下所呈现出的电特性,推导出目标场内部的电导率分布信息,进而推知该场中媒质的分布情况。EIT图像重建问题是一个非线性的病态逆问题,且测量系统往往存在噪声,使重建图像中存在伪影,传统的正则化方法对重建图像伪影的抑制能力有限。本文将一种统计学方法,即最大期望EM(expectation maximization)算法应用于EIT逆问题求解。它将EIT的数学模型转化为非负约束极小化问题,并通过梯度投影简化牛顿算法GPRN(gradient projection-reduced Newton iteration method)求解该问题。与传统的Tikhonov算法和共轭梯度算法CG(conjugate gradient)相比,有效地抑制了重建图像中伪影的产生。仿真和实验结果表明,EIT系统可以通过EM算法获得高质量的重建图像。

Electrical impedance tomography（EIT） technology is based on the physical basis that different mediahave different electrical conductivity. The inverse problem of EIT image reconstruction is a nonlinear and ill-posedproblem.The reconstructed images always have artifacts because the noise in the measure system. Hence the tradi-tional regularization method cannot avoid the artifacts which in reconstructed image by the noise. In this paper,theEIT inverse peoblem will be solved by expectation maximization（EM） method,which is a statistical method. TheEIT mathematical model is transformed into the non-negatively constrained likelihood minimization problem by theEM method. And this problem is solved using gradient projection-reduced Newton（GPRN） iteration method. Com-pared with the conjugate gradient（CG） and the Tikhonov method,both of the simulation and experimental resultsshow that EIT can get better reconstruction results by the EM method. As a result,the EM method can get non-nega-tive solution. Besides,the EM method can avoid the artifacts in the reconstructed images effectively and improvethe quality of the reconstructed images.