Full field inversion in photoacoustic tomography with variable sound speed

TL;DR

This paper introduces a two-step reconstruction method for photoacoustic tomography with full field data that accounts for variable sound speed, improving accuracy over traditional constant sound speed assumptions.

Contribution

It presents a novel two-step approach combining inverse Radon transform and wave inversion, specifically designed for variable sound speed in full field photoacoustic tomography.

Findings

The method accurately reconstructs pressure distributions with variable sound speed.

The iterative wave inversion approach is shown to be unique and stable.

Numerical experiments demonstrate improved reconstruction quality.

Abstract

Recently, a novel measurement setup has been introduced to photoacoustic tomography, that collects data in the form of projections of the full 3D acoustic pressure distribution at a certain time instant. Existing imaging algorithms for this kind of data assume a constant speed of sound. This assumption is not always met in practice and thus leads to erroneous reconstructions. In this paper, we present a two-step reconstruction method for full field detection photoacoustic tomography that takes variable speed of sound into account. In the first step, by applying the inverse Radon transform, the pressure distribution at the measurement time is reconstructed point-wise from the projection data. In the second step, one solves a final time wave inversion problem where the initial pressure distribution is recovered from the known pressure distribution at the measurement time. For the latter problem, we derive an iterative solution approach, compute the required adjoint operator, and show its uniqueness and stability.