Summary: A GENERAL FRAMEWORK FOR ITERATIVE RECONSTRUCTION
ALGORITHMS IN OPTICAL TOMOGRAPHY, USING A FINITE
SIMON R. ARRIDGE \Lambda AND MARTIN SCHWEIGER y
Abstract. In this paper we present several schemes for solving the inverse problem in Opti
cal 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.
Key words. Optical Tomography, Diffusion, Inverse Problems, Finite Elements.
1. Introduction. By Optical Tomography we mean the methodology of using
light in a narrow wavelength band in the nearinfrared (¸700nm1000nm), to tran
silluminate tissue, and to use the resulting measurements of intensity on the tissue
boundary to reconstruct a map of the optical properties within the tissue. This quite
complex field is relatively new, yet has attracted considerable interest from theo
reticians, experimental scientists, and clinicians. Recent developments can be found
in several review articles in the recent Royal Society meeting , and other jour
nals [14, 3].