Recent Developments in Numerical Techniques for Transport-Based Medical Imaging Methods (Communications in Computational Physics, 2010)
The objective of this paper is to review recent developments in numerical reconstructionmethods for inverse transport problems in imaging applications, mainlyoptical tomography, fluorescence tomography and bioluminescence tomography. Inthose inverse problems, one aims at reconstructing physical parameters, such as the absorptioncoefficient, the scattering coefficient and the fluorescence light source, insideheterogeneous media, from partial knowledge of transport solutions on the boundariesof the media. The physical parameters recovered can be used for diagnostic purpose.Numerical reconstruction techniques for those inverse transport problems can beroughly classified into two categories: linear reconstruction methods and nonlinear reconstructionmethods. In the first type of methods, the inverse problems are linearizedaround some known background to obtain linear inverse problems. Classical regularizationtechniques are then applied to solve those inverse problems. The second typeof methods are either based on regularized nonlinear least-square techniques or basedon gradient-driven iterative methods for nonlinear operator equations. In either case,the unknown parameters are iteratively updated until the solutions of the transportequations with the those parameters match the measurements to a certain extent.We review linear and nonlinear reconstruction methods for inverse transport problemsin medical imaging with stationary, frequency-domain and time-dependent data. Thematerials presented include both existing and new results. Meanwhile, we attempt topresent similar algorithms for different problems in the same framework to make itmore straightforward to generalize those algorithms to other inverse (transport) problems.