# A regularized progressive expansion algorithm for recovery of scattering media from
time–resolved data

### J. Chang *et al.* (1997)

#### Summary

Reconstructions of the absorption cross sections of a dense scattering medium 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 occurring at shallower
depths. In order to reduce the sensitivity of the PE algorithm to noise, a Regularized PE (RPE)
algorithm is proposed, which incorporates regularization techniques in the PE algorithm. The PE
and 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 varying strength. The reconstruction results show that the PE and RPE algorithms, when
combined with proper overlapping, can effectively overcome the underdeterminedness of the inverse
problem. The RPE algorithm yields more accurate and stable reconstructions under the same noise
level.