
Proceedings Paper
Localization of point sources for systems governed by the wave equationFormat | Member Price | Non-Member Price |
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Paper Abstract
Analytic sensing has recently been proposed for source localization from boundary measurements using a generalization
of the finite-rate-of-innovation framework. The method is tailored to the quasi-static electromagnetic
approximation, which is commonly used in electroencephalography. In this work, we extend analytic sensing
for physical systems that are governed by the wave equation; i.e., the sources emit signals that travel as waves
through the volume and that are measured at the boundary over time. This source localization problem is highly
ill-posed (i.e., the unicity of the source distribution is not guaranteed) and additional assumptions about the
sources are needed. We assume that the sources can be described with finite number of parameters, particularly,
we consider point sources that are characterized by their position and strength. This assumption makes
the solution unique and turns the problem into parametric estimation. Following the framework of analytic
sensing, we propose a two-step method. In the first step, we extend the reciprocity gap functional concept to
wave-equation based test functions; i.e., well-chosen test functions can relate the boundary measurements to
generalized measure that contain volumetric information about the sources within the domain. In the second
step-again due to the choice of the test functions - we can apply the finite-rate-of-innovation principle; i.e., the
generalized samples can be annihilated by a known filter, thus turning the non-linear source localization problem
into an equivalent root-finding one. We demonstrate the feasibility of our technique for a 3-D spherical geometry.
The performance of the reconstruction algorithm is evaluated in the presence of noise and compared with the
theoretical limit given by Cramer-Rao lower bounds.
Paper Details
Date Published: 27 September 2011
PDF: 11 pages
Proc. SPIE 8138, Wavelets and Sparsity XIV, 81380P (27 September 2011); doi: 10.1117/12.894645
Published in SPIE Proceedings Vol. 8138:
Wavelets and Sparsity XIV
Manos Papadakis; Dimitri Van De Ville; Vivek K. Goyal, Editor(s)
PDF: 11 pages
Proc. SPIE 8138, Wavelets and Sparsity XIV, 81380P (27 September 2011); doi: 10.1117/12.894645
Show Author Affiliations
Zafer Dogan, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Univ. of Geneva (Switzerland)
Vagia Tsiminaki, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Univ. of Geneva (Switzerland)
Ivana Jovanovic, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Univ. of Geneva (Switzerland)
Univ. of Geneva (Switzerland)
Vagia Tsiminaki, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Univ. of Geneva (Switzerland)
Ivana Jovanovic, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Univ. of Geneva (Switzerland)
Thierry Blu, The Chinese Univ. of Hong Kong (Hong Kong, China)
Dimitri Van De Ville, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Univ. of Geneva (Switzerland)
Dimitri Van De Ville, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Univ. of Geneva (Switzerland)
Published in SPIE Proceedings Vol. 8138:
Wavelets and Sparsity XIV
Manos Papadakis; Dimitri Van De Ville; Vivek K. Goyal, Editor(s)
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