Acousto-electric tomography with total variation regularization
Acousto-electric tomography with total variation regularization
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DOI：
10.1088/1361-6420/aaece5
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发表时间：
2018-08
期刊：
影响因子：
2.1
通讯作者：
Bolaji James Adesokan;Bjørn Jensen;Bangti Jin;K. Knudsen
中科院分区：
文献类型：
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作者：
Bolaji James Adesokan;Bjørn Jensen;Bangti Jin;K. Knudsen
我们研究了声电断层扫描中从内部功率密度数据恢复有界域中的电导率分布的数值重建问题。我们提出了一种恢复不连续电导率分布的数值方法，通过将其重新表述为具有 L1 拟合和受 PDE 约束的总变分惩罚的优化问题。我们建立了前向映射的连续性和可微性结果以及优化问题的适定性，并提出了一种基于连续线性化、平滑和迭代重新加权的易于实现且鲁棒的数值方法。进行了大量的数值实验来说明所提出方法的可行性。
We study the numerical reconstruction problem in acousto-electric tomography of recovering the conductivity distribution in a bounded domain from interior power density data. We propose a numerical method for recovering discontinuous conductivity distributions, by reformulating it as an optimization problem with L1 fitting and total variation penalty subject to PDE constraints. We establish continuity and differentiability results for the forward map, and the well-posedness of the optimization problem, and present an easy-to-implement and robust numerical method based on successive linearization, smoothing and iterative reweighting. Extensive numerical experiments are presented to illustrate the feasibility of the proposed approach.