Analytic sensing: direct recovery of point sources from planar Cauchy boundary measurements

D. Kandaswamy; T. Blu; D. Van De Ville

doi:10.1117/12.733823

20 September 2007 Analytic sensing: direct recovery of point sources from planar Cauchy boundary measurements

D. Kandaswamy, T. Blu, D. Van De Ville

Proceedings Volume 6701, Wavelets XII; 67011Y (2007) https://doi.org/10.1117/12.733823
Event: Optical Engineering + Applications, 2007, San Diego, California, United States

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.

Citation Download Citation

D. Kandaswamy, T. Blu, and D. Van De Ville "Analytic sensing: direct recovery of point sources from planar Cauchy boundary measurements", Proc. SPIE 6701, Wavelets XII, 67011Y (20 September 2007); https://doi.org/10.1117/12.733823

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