Regularized Progressive Expansion Algorithm for Recovery of Scattering Media from Time-Resolved Data

Abstract

A principal difficulty encountered in dealing with highly diffused signals is that the inverse problem is ill-posed and often underdetermined. A progressive expansion (PE) algorithm has previously been reported, which has proven to be quite effective in circumventing the underdetermined nature of the inverse problem. However, the PE approach is sensitive to noise. Propagation of errors can become especially severe when evaluating regions deep beneath the surface. Here we describe results of using a Regularized PE (RPE) algorithm, which is shown to exhibit improved stability. The RPE algorithm has been applied to time–resolved data calculated from a perturbation The media tested include isotropically scattering slabs containing one or two compact absorbers at different depths below the surface. The data were corrupted by additive noise with varying strength. Compared to the original PE algorithm, the RPE algorithm has yielded more accurate and stable reconstructions under the same noise level.