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Conference Papers Year : 2013

Reconstruction of solutions to the Helmholtz equation from punctual measurements

Gilles Chardon
Albert Cohen

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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Dates and versions

hal-00842798 , version 1 (09-07-2013)

Identifiers

  • HAL Id : hal-00842798 , version 1

Cite

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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