Implicit learning to determine variable sound speed and the reconstruction operator in photoacoustic tomography

TL;DR

This paper introduces an implicit learning framework for photoacoustic tomography that simultaneously estimates unknown variable sound speed and the reconstruction operator from boundary measurements, improving imaging accuracy.

Contribution

The novel implicit learning approach jointly estimates sound speed and reconstruction operator in PAT using boundary data, addressing a key inverse problem.

Findings

Successfully estimates variable sound speed in PAT.

Accurately reconstructs initial pressure from boundary data.

Demonstrates robustness in experimental results.

Abstract

Photoacoustic tomography (PAT) is a hybrid medical imaging technique that offer high contrast and a high spatial resolution. One challenging mathematical problem associated with PAT is reconstructing the initial pressure of the wave equation from data collected at the specific surface where the detectors are positioned. The study addresses this problem when PAT is modeled by a wave equation with unknown sound speed $c$, which is a function of spatial variables, and under the assumption that both the Dirichlet and Neumann boundary values on the detector surface are measured. In practical, we introduce a novel implicit learning framework to simultaneously estimate the unknown $c$ and the reconstruction operator using only Dirichlet and Neumann boundary measurement data. The experimental results confirm the success of our proposed framework, demonstrating its ability to accurately estimate variable sound speed and the reconstruction operator in PAT.