電阻抗斷層掃描的一種最佳化-最小限度化演算法

A Majorization-Minimization Algorithm for Electrical Impedance Tomography

劉于國(Yu-Guo Liu)

指導教授 ： 陳宜良

國立臺灣大學/理學院/數學研究所/博士(2018年)

https://doi.org/10.6342/NTU201802389

摘要

本論文對電阻抗斷層掃描協同一普遍類型的非光滑正則提出了一統整的最佳化-最小限度化(MM) 演算法，其中包含了稀疏與總變差正則。我們證明此提出之MM 演算法的全域收斂性，且呈現源自模擬數據的數值重建結果。此MM 演算法的數值結果顯示了對目標能量的快速遞減及對內含物的強度和位置有好的估計。此外，我們比較此MM演算法和廣為所用的高斯-牛頓法，此MM 演算法對模擬導電率有較好的逼近。

關鍵字

電阻抗斷層掃描 ； 最佳化-最小限度化演算法

並列摘要

In this paper, a unified majorization-minimization (MM) algorithm is proposed for electrical impedance tomography with a general type of nonsmooth convex regularization, including sparse and total variation regularizations.
We prove the global convergence of the proposed MM algorithm and show numerical reconstructions from simulated data. The numerical results of the MM algorithm show a fast decrease in objective energy and good estimates of the intensity and location of inclusions. Besides, we compare the MM algorithm to the widely used Gauss-Newton method, and the MM algorithm shows better approximation to the simulated conductivity.

並列關鍵字

Electrical impedance tomography ； majorization-minimization algorithm

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