A General Framework for Iterative Reconstruction Algorithms in Optical Tomography, Using a Finite Element Method

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Abstract

In this paper we present several schemes for solving the inverse problem in Optical Tomography. We first set the context of Optical Tomography and discuss alternative photon transport models and measurement schemes. We develop the inverse problem as the optimisation of an objective functions and develop three classes of algorithms fors its solution: Newton methods, linearised methods, and gradient methods. We concentrate on the use numerical methods based on Finite Elements, and discuss how efficient methods may be developed using adjoint solutions. A taxonomy of algorithms is given, with an analysis of their spatial and temporal complexity.