Regularized progressive expansion algorithm for recovery of scattering media from time-resolved data

Reconstructions of the absorption cross sections of dense scattering media from time-resolved data are presented. A progressive expansion (PE) algorithm, similar to a layer-stripping approach, is developed to circumvent the underdeterminedness of the inverse problem. An overlapping scheme, which uses detector readings from several consecutive time intervals, is introduced to reduce the propagation of reconstruction errors that occur at shallower depths. To reduce the sensitivity of the PE algorithm to noise, a regularized progressive expansion (RPE) algorithm is proposed, which incorporates regularization techniques into the PE algorithm. The PE and the RPE algorithms are applied to the problem of image reconstruction from time-resolved data. The test media were isotropically scattering slabs containing one or two compact absorbers at different depths below the surface. The data were corrupted by additive white Gaussian noise with various strengths. The reconstruction results show that the PE and the RPE algorithms, when they are combined by proper overlapping, can effectively overcome the underdeterminedness of the inverse problem. The RPE algorithm yields reconstructions that are more accurate and more stable under the same noise level.