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Mathematics > Analysis of PDEs

arXiv:1804.00724 (math)
[Submitted on 2 Apr 2018]

Title:A regularized weighted least gradient problem for conductivity imaging

Authors:Alexandru Tamasan, Alexander Timonov
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Abstract:We propose and study a regularization method for recovering an approximate electrical conductivity solely from the magnitude of one interior current density field. Without some minimal knowledge of the boundary voltage potential, the problem has been recently shown to have nonunique solutions, thus recovering the exact conductivity is impossible. The method is based on solving a weighted least gradient problem in the subspace of functions of bounded variations with square integrable traces. The computational effectiveness of this method is demonstrated in numerical experiments.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1804.00724 [math.AP]
  (or arXiv:1804.00724v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.00724
Related DOI: https://doi.org/10.1088/1361-6420/aaf2fd

Submission history

From: Alexandru Tamasan [view email]
[v1] Mon, 2 Apr 2018 20:43:50 UTC (144 KB)
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