The inverse conductivity problem via the calculus of functions of bounded variation

被引:3
作者
Charalambopoulos, Antonios [1 ]
Markaki, Vanessa [1 ]
Kourounis, Drosos [2 ]
机构
[1] Natl Tech Univ Athens, Sch Appl Math & Phys Sci, Dept Math, Athens 15780, Greece
[2] NEPLAN AG, Kusnacht, Switzerland
关键词
boundary value problems for second-order elliptic equations; inverse problems; ELECTRICAL-IMPEDANCE TOMOGRAPHY; GLOBAL UNIQUENESS; CALDERON PROBLEM; RECONSTRUCTION ALGORITHM; LEVEL SET; IMPLEMENTATION; STABILITY; REGULARIZATION; PLANE;
D O I
10.1002/mma.6251
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV functions. The space of the functions of bounded variation is recommended here as the most appropriate functional space hosting the conductivity profile under reconstruction. For the numerical investigation of the inversion of the inclusion problem, we propose and implement a suitable minimization scheme of an enriched-constructed herein-functional, by exploiting the inner structure of BV space. Finally, we validate and illustrate our theoretical results with numerical experiments.
引用
收藏
页码:5032 / 5072
页数:41
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