Computational and Applied Math Proseminar

Wednesday, March 27, 12:15 p.m. PSA 206

Alexandra Smirnova

Dept Math & Stats, Georgia State U

Iteratively Regularized Gauss-Newton Method with Parameter Decomposition for 2D Inverse Problem in Optical Tomography

Abstract
A new convergence result for an Iteratively Regularized Gauss Newton (IRGN) algorithm with a Tikhonov regularization term using a seminorm generated by a linear operator is established [SRK07]. The convergence theorem uses an a posteriori stopping rule and a modified source condition, without any restriction on the nonlinearity of the operator.

The theoretical results are illustrated by simulations for a 2D version of the exponentially ill-posed optical tomography inverse problem for the diffusion and absorption coefficient spatial distributions. The modified Tikhonov regularization performs the mapping of the minimization variables, which are the coefficients of the spline expansions for the diffusion and absorption, to physical space. This incorporates the inherently differing scales of these variables in the minimization, and also suggests relative weighting of the regularization terms with respect to each parameter space. The presented modification of the IRGN allows greater flexibility for implementations of IRGN solutions of ill-posed inverse problems in which differing scales in physical space hinder standard IRGN inversions.

For further information please contact: mittelmann@asu.edu