Acoustical inverse problems regularization: direct definition of filter factors using Signal-to-Noise Ratio

Philippe Gauthier , Anthony Gerard , Cedric Camier , Alain Berry (1)

1 UdeS - Département de génie mécanique [Sherbrooke]

Acoustic imaging aims at localization and characterization of sound sources using microphone arrays. In this paper a new regularization method for acoustic imaging by inverse approach is proposed. The method first relies on the singular value decomposition of the plant matrix and on the projection of the measured data on the corresponding singular vectors. In place of regularization using classical methods such as truncated singular value decomposition and Tikhonov regularization, the proposed method involves the direct definition of the filter factors on the basis of a thresholding operation, defined from the estimated measurement noise. The thresholding operation is achieved using modified filter functions. This has the advantage of symplifying the selection of the best regularization amount. Theoretical results show that this method is promising, in terms of ease of implementation and accuracy of results, in comparison with Tikhonov regularization and truncated singular value decomposition.

Mots clés: inverse problem; regularization; filter factor; signal to noise ratio

Domaines: Acoustique [physics.class-ph]

Philippe Gauthier, Anthony Gerard, Cedric Camier, Alain Berry. Acoustical inverse problems regularization: direct definition of filter factors using Signal-to-Noise Ratio. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00810862⟩