Analytic sensing: Direct recovery of point sources from planar Cauchy boundary measurements
Journal
Proceedings of SPIE - The International Society for Optical Engineering
Journal Volume
6701
ISBN
9780819468499
Date Issued
2007-12-01
Author(s)
Abstract
Inverse problems play an important role in engineering. A problem that often occurs in electromagnetics (e.g. EEG) is the estimation of the locations and strengths of point sources from boundary data. We propose a new technique, for which we coin the term "analytic sensing". First, generalized measures are obtained by applying Green's theorem to selected functions that are analytic in a given domain and at the same time localized to "sense" the sources. Second, we use the finite-rate-of-innovation framework to determine the locations of the sources. Hence, we construct a polynomial whose roots are the sources' locations. Finally, the strengths of the sources are found by solving a linear system of equations. Preliminary results, using synthetic data, demonstrate the feasibility of the proposed method.
Subjects
Analytic functions | Annihilating filters | Laplace's equation | Source localization
SDGs
Type
conference paper