# Recovery of optical cross–section perturbations in dense–scattering media using transport–theory–based imaging operators and steady–state simulated data

### J. Chang *et al.* (1996)

#### Summary

We present a useful strategy for imaging perturbations of the macroscopic absorption cross
section of dense scattering media using steady–state light sources. A perturbation model based on
transport theory is derived and the inverse problem is simplified to a system of linear equations,
**W**Δ*μ* = Δ**R**, where **W** is the weight matrix,
Δ*μ* is a vector of the unknown perturbations, and Δ**R** is the vector
of detector readings. Monte Carlo simulations (MCS) compute the photon flux across the surfaces of
phantoms containing simple or complex inhomogeneities. Calculation of the weight matrix is also
based upon the results of MCS. Three reconstruction algorithms — conjugate gradient descent,
projection onto convex sets and simultaneous algebraic reconstruction technique, with or without
imposed positivity constraints — are used for image reconstruction. A rescaling technique that
improves the conditioning of the weight matrix is also developed. Results show that the analysis
of time–independent data using a perturbation model is capable of resolving the internal structure
of a dense scattering medium. Imposition of positivity constraints improves image quality at the
cost of a reduced convergence rate. Use of the rescaling technique increases the initial rate of
convergence, resulting in accurate images in a smaller number of iterations.