Multiwave tomography in a closed domain: averaged sharp time reversal. (14th May 2015)

• Record Type: Journal Article
• Authors: Stefanov, Plamen; Yang, Yang
• Is Part Of: Inverse problems. Volume 31:Number 6(2015:Jun.)
• Publication Date: 2015-05-14
• Subjects: multiwave tomography -- thermoacoustic tomography -- time reversal; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/6/065007
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We study the mathematical model of multiwave tomography including thermo and photoacoustic tomography with a variable speed for a fixed time interval . We assume that the waves reflect from the boundary of the domain. We propose an averaged sharp time reversal algorithm. In case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann series expansion. When the measurements are taken on a part of the boundary, we show that the same algorithm produces a parametrix. We present numerical reconstructions in both the full boundary and the partial boundary data case.