样本训练算法在电磁层析图像重建中的设计及应用
Design and application of sample training algorithm in electromagnetic tomography image reconstruction

摘要 在电磁层析成像(EMT)领域,病态矩阵方程逆问题求解是图像重建较为重要的一步.本文对截断奇异值分解(TSVD)算法和Tikhonov正则化法求解病态矩阵方程EMT逆问题中的参数选取问题做重点讨论.提出一种新的基于样本图像相关系数最大化的参数选取算法,在与原有参数选取算法的对比中分析其可行性.并将本文提出的灵敏度矩阵包含的多样本特点,应用到L曲线法和广义交叉验证法等算法中,利用统计方法提高灵敏度矩阵方程解稳定性,在一定程度上预防单样本求解导致的偶然性误差.应用硬件成像平台展示所提算法实际成像效果，并分析奇异值抑制方式和截取方式在EMT逆问题的实际应用和参数计算中的优势和劣势.实验数据表明:本文算法在测试样本中有更好的成像效果.
Abstract：In the field of Electromagnetic Tomography (EMT), solving inverse problem of ill-conditioned matrix equation is an important step in image reconstruction. This paper focuses on the parameter selection in the EMT inverse problem of the ill-conditioned matrix equation with Truncated Singular Value Decomposition (TSVD) algorithm and Tikhonov regularization method. It presents a new parameter selection algorithm based on maximizing the correlation coefficients of the sample image and its feasibility is analyzed in contrast with the original parameter selection algorithm. The multi-sample characteristics of the sensitivity matrix presented in this paper are applied to the algorithms of L-curve and generalized cross-validation. The statistical methods are used to improve the stability of the sensitivity matrix equation and to prevent accidental errors caused by single sample solution to a certain extent. Finally, a hardware imaging platform is built to demonstrate the actual imaging effect of the proposed algorithm. The advantages and disadvantages of singular value restraining mode and interception mode in the practical application and parameter calculation of EMT inverse problem are also briefly discussed.The experimental results show that the proposed algorithm has better imaging effect in the test samples.