Photoacoustic inversion formulas using mixed data on finite time intervals

TL;DR

This paper develops explicit photoacoustic inversion formulas for mixed data on finite time intervals, enabling exact reconstruction in convex domains and improving practical applicability in real-world PAT scenarios.

Contribution

It extends previous inversion formulas to finite time data and convex domains, providing explicit formulas and numerical validation for practical photoacoustic tomography.

Findings

Exact reconstruction formulas derived for finite time data

Numerical reconstructions demonstrate effectiveness of the formulas

Comparison shows advantages over previous unlimited time methods

Abstract

We study the inverse source problem in photoacoustic tomography (PAT) for mixed data, which denote a weighted linear combination of the acoustic pressure and its normal derivative on an observation surface. We consider in particular the case where the data are only available on finite time intervals, which accounts for real-world usage of PAT where data are only feasible within a certain time interval. Extending our previous work, we derive explicit formulas up to a smoothing integral on convex domains with a smooth boundary, yielding exact reconstruction for circular or elliptical domains. We also present numerical reconstructions of our new exact inversion formulas on finite time intervals and compare them with the reconstructions of our previous formulas for unlimited time wave measurements.