Analysis for Full Field Photoacoustic Tomography with Variable Sound Speed

TL;DR

This paper develops mathematical foundations for full-field photoacoustic tomography with variable sound speed, establishing uniqueness, stability, and an exact time-reversal inversion method for high-resolution imaging.

Contribution

It introduces the first rigorous analysis of full-field PAT with variable sound speed, including uniqueness, stability, and an exact inversion technique.

Findings

Proves uniqueness and stability of the full-field PAT problem with variable sound speed.

Develops an exact time-reversal based inversion method.

Demonstrates high-resolution imaging potential of the approach.

Abstract

Photoacoustic tomography (PAT) is a non-invasive imaging modality that requires recovering the initial data of the wave equation from certain measurements of the solution outside the object. In the standard PAT measurement setup, the used data consist of time-dependent signals measured on an observation surface. In contrast, the measured data from the recently invented full-field detection technique provide the solution of the wave equation on a spatial domain at a single instant in time. While reconstruction using classical PAT data has been extensively studied, not much is known for the full field PAT problem. In this paper, we build mathematical foundations of the latter problem for variable sound speed and settle its uniqueness and stability. Moreover, we introduce an exact inversion method using time-reversal and study its convergence. Our results demonstrate the suitability of both the full field approach and the proposed time-reversal technique for high resolution photoacoustic imaging.