On the optimal choice of the illumination function in photoacoustic tomography

TL;DR

This paper investigates optimizing the laser excitation function in photoacoustic tomography to improve source reconstruction, employing Bayesian methods, optimal experimental design, and numerical validation for models with fractional damping.

Contribution

It introduces a Bayesian framework with explicit adjoint operator derivation and applies A-optimality for designing the excitation function in photoacoustic tomography.

Findings

Enhanced reconstruction accuracy through optimized excitation functions.

Effective approximation scheme for the cost functional.

Numerical results demonstrating the method's efficacy.

Abstract

This work studies the inverse problem of photoacoustic tomography (more precisely, the acoustic subproblem) as the identification of a space-dependent source parameter. The model consists of a wave equation involving a time-fractional damping term to account for power law frequency dependence of the attenuation, as relevant in ultrasonics. We solve the inverse problem in a Bayesian framework using a Maximum A Posteriori (MAP) estimate, and for this purpose derive an explicit expression for the adjoint operator. On top of this, we consider optimization of the choice of the laser excitation function, which is the time-dependent part of the source in this model, to enhance the reconstruction result. The method employs the $A$-optimality criterion for Bayesian optimal experimental design with Gaussian prior and Gaussian noise. To efficiently approximate the cost functional, we introduce an approximation scheme based on projection onto finite-dimensional subspaces. Finally, we present numerical results that illustrate the theory.