Thermo and photoacoustic Tomography with variable speed and planar detectors

TL;DR

This paper studies a mathematical model for multiwave tomography using variable speed and planar detectors, establishing uniqueness, stability, and a time reversal method to recover singularities from measurements.

Contribution

It introduces a new analysis of multiwave tomography with variable speed and planar detectors, providing sharp estimates and a reconstruction algorithm.

Findings

Proved sharp uniqueness and stability estimates for the model.

Developed a time reversal algorithm for recovering visible singularities.

Validated the approach with theoretical guarantees.

Abstract

We analyze the mathematical model of multiwave tomography with a variable speed with integrating measurements on planes tangent to a sphere surrounding the source. We prove sharp uniqueness and stability estimates with full and partial data and propose a time reversal algorithm which recovers the visible singularities.