A Reciprocity-Law-Compliant Photoacoustic Forward-Adjoint Operator

TL;DR

This paper develops a reciprocity-law-compliant forward-adjoint operator framework for photoacoustic tomography, enabling accurate reconstruction of initial pressure distributions from boundary data.

Contribution

It introduces a novel composite forward operator with a scaled reception operator, ensuring reciprocity compliance and improved reconstruction accuracy.

Findings

The operator pair satisfies an inner-product relation verified numerically.

Regularization of singularities improves stability of the operator.

Iterative minimization yields accurate initial pressure reconstructions.

Abstract

We extend the forward-adjoint operator framework derived in our previous study to photoacoustic tomography (PAT). In that earlier work, the acoustic forward operator included a reception operator that maps, at each time step, the pressure wavefield in free space onto the boundary (receiver surface). It was shown that this reception operator serves as a left-inverse of an emission operator that maps the pressure restricted to the boundary (emitter surface) onto free space, perfectly complying with the reciprocity law of physics. In this study, we define the full PAT forward operator as a composite mapping composed of an acoustic forward operator equipped with a scaled variant of the previously proposed reception operator, and an operator describing the photoacoustic source. Singularities arising both in the reception step (due to the boundary restriction) and in the photoacoustic source (due to its instantaneous nature) are regularized using regularized Dirac delta distributions. The resulting PAT forward-adjoint operator pair satisfies an inner-product relation, which we verify through numerical experiments on a discretized domain. The effectiveness of the proposed operator pair is further demonstrated using an iterative minimization framework that yields both qualitatively and quantitatively accurate reconstructions of an initial pressure distribution from the corresponding Dirichlet-type boundary data.