Recovery guarantees for compressed sensing photoacoustic tomography

TL;DR

This paper establishes stable recovery guarantees in compressed sensing photoacoustic tomography by leveraging signal sparsity and boundary-restricted data, advancing theoretical understanding of inverse wave problems.

Contribution

It introduces the first rigorous stable recovery guarantees for photoacoustic tomography with limited boundary data under sparsity assumptions.

Findings

Stable recovery is possible with boundary-restricted spatial averages.

The framework generalizes existing approaches in the literature.

Refined stability estimates support the theoretical guarantees.

Abstract

Photoacoustic tomography is an emerging medical imaging technology whose primary aim is to map the high-contrast optical properties of biological tissues by leveraging high-resolution ultrasound measurements. Mathematically, this can be framed as an inverse source problem for the wave equation over a specific domain. In this work, for the first time, it is shown how, by assuming signal sparsity, it is possible to establish rigorous stable recovery guarantees when the data collection is given by spatial averages restricted to a limited portion of the boundary. Our framework encompasses many approaches that have been considered in the literature. The result is a consequence of a general framework for subsampled inverse problems developed in previous works and refined stability estimates for an inverse problem for the wave equation with surface measurements.