KEYWORDS: Sensors, Data modeling, Inverse problems, Electromagnetism, Electroencephalography, Biomedical optics, 3D modeling, Mathematical modeling, Statistical analysis, Signal to noise ratio
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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