Acoustical inverse problems regularization: Direct definition of filter factors using Signal-to-Noise Ratio
2014
Abstract 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 decompositionof the plant matrix and on the projection of the measured data on the corresponding
singularvectors. In place of regularization using classical methods such as truncated
singular value decompositionand
Tikhonov regularization, the proposed method involves the direct definition of the
filter factorson 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 factorwhich provides more damping to the
singularcomponents 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 regularizationand truncated
singular value decomposition.
Keywords:
- Singular value decomposition
- Tikhonov regularization
- Signal-to-noise ratio
- Control theory
- Regularization perspectives on support vector machines
- Inverse problem
- Backus–Gilbert method
- Regularization (mathematics)
- Mathematical optimization
- Filter factor
- Mathematics
- Algorithm
- Thresholding
- Mathematical analysis
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