Full Field Inversion of the Attenuated Wave Equation: Theory and Numerical Inversion

TL;DR

This paper investigates the mathematical theory and numerical methods for full-field photoacoustic tomography, focusing on the unique and stable inversion of wave data with variable sound speed and damping, supported by simulations.

Contribution

It provides the first theoretical analysis of uniqueness and stability for full-field PAT with variable coefficients and develops new iterative and variational algorithms for numerical inversion.

Findings

Proved uniqueness and stability of the inversion problem.

Developed iterative and variational algorithms for numerical reconstruction.

Validated methods with numerical simulations for different data angles.

Abstract

Standard photoacoustic tomography (PAT) provides data that consist of time-dependent signals governed by the wave equation, which are measured on an observation surface. In contrast, the measured data from the recently invented full-field PAT is the Radon transform of 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 about the full-field PAT problem. In this paper, we study full-field photoacoustic tomography with spatially variable sound speed and spatially variable damping. In particular, we prove the uniqueness and stability of the associated single-time full-field wave inversion problem and develop algorithms for its numerical inversion using iterative and variational regularization methods. Numerical simulations are presented for both full-angle and limited-angle data cases