Regularization approaches for quantitative photoacoustic tomography using the radiative transfer equation

TL;DR

This paper investigates the mathematical properties of the forward operator in quantitative photoacoustic tomography (QPAT) and proposes Tikhonov-type regularization methods to solve the nonlinear, ill-posed optical inverse problem.

Contribution

It provides theoretical analysis of the forward operator in QPAT and introduces regularization approaches considering physical, numerical, and smoothness assumptions.

Findings

Proved properties of the forward operator in QPAT

Established conditions for regularized solutions

Analyzed physical and numerical aspects of regularization

Abstract

Quantitative Photoacoustic tomography (QPAT) is an emerging medical imaging modality which offers the possibility of combining the high resolution of the acoustic waves and large contrast of optical waves by quantifying the molecular concentration in biological tissue. In this paper, we prove properties of the forward operator that associate optical parameters from measurements of a reconstructed Photoacoustic image. This is often referred to as the optical inverse problem, that is nonlinear and ill-posed. The proved properties of the forward operator provide sufficient conditions to show regularized properties of approximated solutions obtained by Tikhonov-type approaches. The proposed Tikhonov- type approaches analyzed in this contribution are concerned with physical and numerical issues as well as with \textit{a priori} information on the smoothness of the optical coefficients for with (PAT) is particularly a well-suited imaging modality.