基于改进型迭代NR的磁感应断层成像图像重建算法

doi:10.3969/j.issn.0258-8021.2015. 02.009

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摘要在磁感应断层成像中，图像重建是一个典型的病态问题，其数值解存在不稳定性。针对此问题，提出一种基于加权矩阵和L1范数正则化的改进型迭代NewtonRaphson (NR)算法。该算法通过在目标函数的误差项中引入加权矩阵，同时在L2范数正则化惩罚项的基础上引入L1范数正则化，改善图像重建解的病态性。设置3种典型的模型，分别对有无噪声的数据进行分析，将本算法与Tikhonov正则化算法和迭代NR算法进行对比。在无噪声数据分析中，所提算法相对Tikhonov正则化算法和迭代NR算法的相对图像误差减小011～014，相关系数提高13%～17%。在有噪声数据中，所提算法相对于Tikhonov正则化算法和迭代NR算法的相对图像误差减小006～009，相关系数提高7%～10%。提出的算法成像性能较好，且抗噪性能较强，为进一步的实验重建精确性提供理论依据。

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	韩敏^1*薛玉艳¹秦攀¹韩杰²姜长斌²

关键词 ：磁感应断层成像, 图像重建, L1范数正则化, 迭代NewtonRaphson

Abstract：The image reconstruction process is a typical illposed problem in magnetic induction tomography (MIT), in which the numerical solution is unstable. To solve this problem, an improved iteration NewtonRaphson algorithm based on weighted matrix and L1norm regularization is improved. The proposed method adds the weight matrix in the objective function and adds L1norm regularization term in L2norm regularization penalty term. The analysis is made for three typical models in the data with and without noise, respectively. And the proposed algorithm is contrasted with Tikhonov regularization algorithm and iterative NR algorithm. In the data without noise, relative to Tikhonov regularization algorithm and iterative NR algorithm, the relative error is reduced by 011-014. And then, the correlation coefficient is raised by 13%-17%. The algorithm has good performance in imaging. In the data with noise, the relative error is reduced by 006-009, and the correlation coefficient is raised by 7%-10% in the proposed algorithm. The algorithm has good antinoise performance, which has offered theory basis for the study of reconstruction accuracy.

Key words： magnetic induction tomography (MIT) image reconstruction L1norm regularization iteration NewtonRaphson

基金资助:中央高校基本科研业务费专项项目（DUT13JB08）；大连市科技局科技计划项目（2012C014）

引用本文:

韩敏^1*薛玉艳¹秦攀¹韩杰²姜长斌². 基于改进型迭代NR的磁感应断层成像图像重建算法[J]. 中国生物医学工程学报, 2015, 34(2): 190-197.
Han Min^1*Xue Yuyan¹Qin Pan¹Han Jie. An Improved Image Reconstruction Algorithm Based on Iteration NR in Magnetic Induction Tomography. journal1, 2015, 34(2): 190-197.

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http://cjbme.csbme.org/CN/10.3969/j.issn.0258-8021.2015. 02.009 或 http://cjbme.csbme.org/CN/Y2015/V34/I2/190

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