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Title: A regularized weighted least gradient problem for conductivity imaging
We propose and study a method for imaging an approximate electrical conductivity from the magnitude of one interior current density field without any knowledge of the boundary voltage potential. Solely from this interior data, the exact conductivity is impossible to recover as non-unique solutions exist. We propose a method to recover a minimum residual type solution. The method is based on a weighted least gradient problem in the subspace of functions of bounded variations with square integrable traces. We prove existence and uniqueness for a nearby problem, and study the continuous dependence data for a regularized problem. The computational effectiveness and numerica  more » « less
Award ID(s):
1818882
PAR ID:
10093091
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Inverse problems
Volume:
35
Issue:
4
ISSN:
1361-6420
Page Range / eLocation ID:
045006(20pp)
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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