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

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. The originality of the approach is to propose the definition of a filter factor which provides more damping to the singular components dominated by noise than that given by the Tikhonov filter. This has the advantage of potentially simplifying the selection of the best regularization amount in inverse problems. Theoretical results show that this method is comparatively more accurate than Tikhonov regularization and truncated singular value decomposition.