Analytic Sensing: Direct Recovery of Point Sources from Planar Cauchy Boundary Measurements

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.

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Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet XII, 2, San Diego CA, USA, 67011Y-1–67011Y-6

 Record created 2015-09-18, last modified 2018-12-03

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