Acousto-electric tomography with total variation regularization. (4th February 2019)

• Record Type: Journal Article
• Authors: Adesokan, Bolaji James; Jensen, Bjørn; Jin, Bangti; Knudsen, Kim
• Is Part Of: Inverse problems. Volume 35:Number 3(2019)
• Publication Date: 2019-02-04
• Subjects: acousto-electric tomography -- reconstruction -- total variation; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aaece5
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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 L 1 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.