Local Inversions in Ultrasound Modulated Optical Tomography

TL;DR

This paper investigates the local uniqueness and stability of reconstructing optical properties in ultrasound modulated optical tomography, proposing conditions and an iterative method for solving the inverse problem.

Contribution

It provides new sufficient conditions for local reconstruction stability and introduces an iterative approach based on linear elliptic systems.

Findings

Established conditions for local uniqueness and stability

Developed an iterative reconstruction algorithm

Analyzed linear elliptic systems for inverse problem solving

Abstract

Ultrasound modulated optical tomography, also called acousto-optics tomography, is a hybrid imaging modality that aims to combine the high contrast of optical waves with the high resolution of ultrasound. We follow the model of the influence of ultrasound modulation on the light intensity measurements developed in [Bal Schotland PRL 2010]. We present sufficient conditions ensuring that the absorption and diffusion coefficients modeling light propagation can locally be uniquely and stably reconstructed from the corresponding available information. We present an iterative procedure to solve such a problem based on the analysis of linear elliptic systems of redundant partial differential equations.