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Conference Papers Year : 2013

Reconstruction of solutions to the Helmholtz equation from punctual measurements

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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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