This dissertation studies methods for inverse source problems in diffuse imaging. The convex source support method for the Poisson's equation is extended to the two-dimensional half-space and a ball in three dimensions. The related problems of detecting inhomogeneities in electrical impedance tomography are discussed, as well. In addition to using the conventional measurements consisting of one or more Cauchy data pairs, sweep data, a novel measurement configuration compatible with the convex source support algorithm, is proposed and analyzed. This treatise also considers an amalgamation of non-linear Tikhonov regularization and preconditioned Krylov subspace methods. The lagged diffusivity fixed point iteration is used to produce a sequence of least-squares problems with linearized regularizers. These regularizers are recast as preconditions. A modified version of the LSQR algorithm is derived, allowing efficient use of the introduced preconditions. While the performance of the resulting algorithm is tested on fluorescence diffuse optical tomography, the method is directly applicable to other linear inverse problems, as well.
|Translated title of the contribution||Käänteislähdemenetelmiä diffusiiviseen kuvantamiseen|
|Publication status||Published - 2013|
|MoE publication type||G5 Doctoral dissertation (article)|
- inverse source problems
- electrical impedance tomography
- convex source support