On time reversal in photoacoustic tomography for tissue similar to water

TL;DR

This paper demonstrates that regularized time reversal can effectively reconstruct initial pressure in photoacoustic tomography within water-like dissipative media, offering a practical alternative to causal methods.

Contribution

It introduces a modified time reversal approach using time-shifted causal data for dissipative media similar to water, supported by theoretical and numerical validation.

Findings

Time reversal with shifted data approximates initial pressure in water-like media.

Regularized time reversal improves image quality despite dissipation.

The method provides an alternative to existing causal approaches.

Abstract

This paper is concerned with time reversal in \emph{photoacoustic tomography} (PAT) of dissipative media that are similar to water. Under an appropriate condition, it is shown that the time reversal method in \cite{Wa11,AmBrGaWa11} based on the non-causal thermo-viscous wave equation can be used if the non-causal data is replaced by a \emph{time shifted} set of causal data. We investigate a similar imaging functional for time reversal and an operator equation with the time reversal image as right hand side. If required, an enhanced image can be obtained by solving this operator equation. Although time reversal (for noise-free data) does not lead to the exact initial pressure function, the theoretical and numerical results of this paper show that regularized time reversal in dissipative media similar to water is a valuable method. We note that the presented time reversal method can be considered as an alternative to the causal approach in \cite{KaSc13} and a similar operator equation may hold for their approach.