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

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

Proceedings of the SPIE Optics and Photonics 2007 Conference on Mathematical Methods: Wavelet XII, San Diego CA, USA, August 26-29, 2007, vol. 6701, pp. 67011Y-1/67011Y-6.



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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