Accession Number : ADA567454
Title : Analysis of the Hessian for Inverse Scattering Problems. Part 3. Inverse Medium Scattering of Electromagnetic Waves in Three Dimensions
Descriptive Note : Technical rept.
Corporate Author : TEXAS UNIV AT AUSTIN INST FOR COMPUTATIONAL ENGINEERING AND SCIENCES
Personal Author(s) : Bui-Thanh, Tan ; Ghattas, Omar
Report Date : Aug 2012
Pagination or Media Count : 17
Abstract : Continuing our previous work [6, Inverse Problems, 2012, 28, 055002] and [5, Inverse Problems, 2012, 28, 055001], we address the ill-posedness of the inverse scattering problem of electromagnetic waves due to an inhomogeneous medium by studying the Hessian of the data mis t. We derive and analyze the Hessian in both H older and Sobolev spaces. Using an integral equation approach based on Newton potential theory and compact embeddings in H older and Sobolev spaces we show that the Hessian can be decomposed into three components, all of which are shown to be compact operators. The implication of the compactness of the Hessian is that for small data noise and model error, the discrete Hessian can be approximated by a low-rank matrix. This in turn enables fast solution of an appropriately regularized inverse problem, as well as Gaussian-based quanti cation of uncertainty in the estimated inhomogeneity.
Descriptors : *ELECTROMAGNETIC SCATTERING , *INVERSE SCATTERING , INTEGRAL EQUATIONS , INVERSE PROBLEMS , OPTIMIZATION , POTENTIAL THEORY , THREE DIMENSIONAL
Subject Categories : Numerical Mathematics
Radiofrequency Wave Propagation
Distribution Statement : APPROVED FOR PUBLIC RELEASE