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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
Last modification on : Friday, December 3, 2021 - 11:43:37 AM
Long-term archiving on: : Wednesday, April 5, 2017 - 8:57:32 AM


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  • HAL Id : hal-00842798, version 1


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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