Reconstruction of solutions to the Helmholtz equation from punctual measurements

Abstract : We analyze the sampling of solutions to the Helmholtz equation (e.g. sound fields in the harmonic regime) using a least-squares method based on approximations of the solutions by sums of Fourier-Bessel functions or plane waves. This method compares favorably to others such as Orthogonal Matching Pursuit with a Fourier dictionary. We show that using a significant proportion of samples on the border of the domain of interest improves the stability of the reconstruction, and that using cross-validation to estimate the model order yields good reconstruction results.
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Submitted on : Tuesday, July 9, 2013 - 2:33:21 PM
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Gilles Chardon, Albert Cohen, Laurent Daudet. Reconstruction of solutions to the Helmholtz equation from punctual measurements. SampTA - Sampling Theory and Applications 2013, Jul 2013, Bremen, Germany. ⟨hal-00842798⟩

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