Reconstruction formulas for Photoacoustic Imaging in Attenuating Media

TL;DR

This paper develops explicit reconstruction formulas for photoacoustic imaging in weakly attenuating media, analyzes their stability, and demonstrates their effectiveness through numerical experiments.

Contribution

It introduces new explicit formulas for photoacoustic inversion in attenuating media and provides a numerical algorithm validated by experiments.

Findings

Reconstruction formulas are moderately ill-posed.

Numerical algorithm successfully images in attenuating media.

Feasibility demonstrated through numerical experiments.

Abstract

In this paper we study the problem of photoacoustic inversion in a weakly attenuating medium. We present explicit reconstruction formulas in such media and show that the inversion based on such formulas is moderately ill--posed. Moreover, we present a numerical algorithm for imaging and demonstrate in numerical experiments the feasibility of this approach.