Shape reconstruction in scattering media with voids using a transport model and level sets

TL;DR

This paper introduces a two-step shape reconstruction method for diffuse optical tomography that combines transport modeling, adjoint fields, and level set techniques to accurately recover obstacles within scattering media.

Contribution

It presents a novel two-step approach integrating transport-backtransport and level set methods with adjoint fields for efficient shape reconstruction in DOT.

Findings

Fast and accurate recovery of multiple objects

Effective handling of clear regions in the medium

Low-contrast approximation as initial guess

Abstract

A two-step shape reconstruction method for diffuse optical tomography (DOT) is presented which uses adjoint fields and level sets. The propagation of near-infrared photons in tissue is modeled by the time-dependent linear transport equation, of which the absorption parameter has to be reconstructed from boundary measurements. In the shape reconstruction approach, it is assumed that the inhomogeneous background absorption parameter and the values inside the obstacles (which typically have a high contrast to the background) are known, but that the number, sizes, shapes, and locations of these obstacles have to be reconstructed from the data. An additional difficulty arises due to the presence of so-called clear regions in the medium. The first step of the reconstruction scheme is a transport-backtransport (TBT) method which provides us with a low-contrast approximation to the sought objects. The second step uses this result as an initial guess for solving the shape reconstruction problem. A key point in this second step is the fusion of the 'level set technique' for representing the shapes of the reconstructed obstacles, and an 'adjoint-field technique' for solving the nonlinear inverse problem. Numerical experiments are presented which show that this novel method is able to recover one or more objects very fast and with good accuracy.