Time reversal in photoacoustic tomography and levitation in a cavity

TL;DR

This paper explores advanced photoacoustic imaging techniques using time reversal and spherical mean transforms, demonstrating exact reconstruction in specific geometries and discussing non-uniqueness issues in inverse problems.

Contribution

It introduces a class of geometries where exact filtered back projection reconstruction is possible and interprets this as a time reversal mirror in photoacoustic tomography.

Findings

Exact reconstruction formulas for specific geometries

Interpretation of reconstruction as a time reversal mirror

Examples of non-uniqueness in inverse potential problems

Abstract

A class of photoacoustic acquisition geometries in n-space is considered such that the spherical mean transform admits an exact filtered back projection reconstruction formula. The reconstruction is interpreted as a time reversion mirror that reproduces exactly an arbitrary source distribution in the cavity. A series of examples of non-uniqueness of the inverse potential problem is constructed basing on the same geometrical technique.