A variational method for quantitative photoacoustic tomography with piecewise constant coefficients
Abstract
In this article, we consider the inverse problem of determining spatially heterogeneous absorption and diffusion coefficients from a single measurement of the absorbed energy (in the steady-state diffusion approximation of light transfer). This problem, which is central in quantitative photoacoustic tomography, is in general ill-posed since it admits an infinite number of solution pairs. We show that when the coefficients are known to be piecewise constant functions, a unique solution can be obtained. For the numerical determination of the coefficients, we suggest a variational method based based on an Ambrosio-Tortorelli-approximation of a Mumford-Shah-like functional, which we implemented numerically and tested on simulated two-dimensional data.
Cite
@article{arxiv.1509.04982,
title = {A variational method for quantitative photoacoustic tomography with piecewise constant coefficients},
author = {Elena Beretta and Monika Muszkieta and Wolf Naetar and Otmar Scherzer},
journal= {arXiv preprint arXiv:1509.04982},
year = {2015}
}