Wolfgang Bangerth, Amit Joshi
Optical tomography attempts to determine a spatially variable coefficient in
the interior of a body from measurements of light fluxes at the boundary.
Like in many other applications in biomedical imaging, computing solutions
in optical tomography is complicated by the fact that one wants to identify
an unknown number of relatively small irregularities in this coefficient at
unknown locations, for example corresponding to the presence of tumors. To
recover them at the resolution needed in clinical practice, one has to use
meshes that, if uniformly fine, would lead to intractably large problems
with hundreds of millions of unknowns.
Adaptive finite element methods for the solution of
inverse problems in optical tomography
Inverse Problems, vol. 24 (2008), pp. 034011/1-22.
This article was selected for the
Board Highlights 2008.
Adaptive meshes are therefore an indispensable tool. In this paper, we will
describe a framework for the adaptive finite element solution of optical
tomography problems. It takes into account all steps starting from the
formulation of the problem including constraints on the coefficient, outer
Newton-type nonlinear and inner linear iterations, regularization, and
in particular the interplay of these algorithms with discretizing the
problem on a sequence of adaptively refined meshes.
We will demonstrate the efficiency and accuracy of these algorithms on a set
of numerical examples of clinical relevance related to locating lymph nodes
in tumor diagnosis.
Thu May 4 14:55:18 MDT 2017