Approximations parcimonieuses et problèmes inverses en acoustique

Abstract : In this work, we construct sparse approximations of acoustic fields, as well as methods for solving inverse problems based on these approximations. The approximation of solutions of the Helmholtz equation is extended to the solutions of plate vibration models, which allows the design of an alternative numerical method for the computation of plate eigenmodes. Some inverse problems are then studied, using these approximations results. The first is nearfield acoustical holography, for which we develop a new regularisation scheme, as well as a random antenna. These two tools allow the reduction of the number of measurements needed for a good reconstruction of the operational deflection shapes to be recovered. Spatial interpolation of plate impulse responses is then studied. Using the approximation models, we show that we can measure the plate impulse responses with fewer measurements than needed by the Shannon sampling theorem, by choosing the sampling strategy justified by a theoretical analysis. Finally, we developped new algorithms for source localisation in an enclosed space. We show that using approximation models of acoustical fields, source localisation is possible without any prior on the space where the waves propagate.
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Submitted on : Monday, September 17, 2012 - 11:20:57 AM
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Gilles Chardon. Approximations parcimonieuses et problèmes inverses en acoustique. Optique [physics.optics]. Université Pierre et Marie Curie - Paris VI, 2012. Français. ⟨pastel-00732847⟩

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