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arXiv · 1509.04982

A variational method for quantitative photoacoustic tomography with piecewise constant coefficients

Elena Beretta·Monika Muszkieta·Wolf Naetar·Otmar Scherzer
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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.

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Elena Beretta, Monika Muszkieta, Wolf Naetar, Otmar Scherzer. 2015-09-16. A variational method for quantitative photoacoustic tomography with piecewise constant coefficients. https://arxiv.org/abs/1509.04982

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