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

Abstract

1377Acoustic 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. It has the advantage of simplifying 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.

A New Method for Determining Optimal Regularization Parameter in Near‐Field Acoustic Holography

“…The minimization problem related to (15) can be solved by one-dimensional search technique, which is exactly the same as the L-curve method in the Matlab package developed by Hansen [30]. In order to capture the optimal solution more easily in the search interval, the logarithmic scale coordinate is also used to ensure that the curve of ‖Q 2 ‖ 2 with can be flat and broad in the vicinity of the optimal solution.…”

“…Consequently, the reconstruction stability is a key problem in NAH technology due to the fact that the realization process is ill-posed and the reconstructed results are highly sensitive to signal-to-noise ratio (SNR) [15]. If the conventional method for solving inverse matrix from the source to the hologram surface is used directly, the measurement error on the hologram surface as the input may be amplified sharply, and even the reconstructed results are completely unavailable.…”

Sound fields separation and reconstruction of irregularly shaped sources

“…The Tikhonov lter factor is smoother and continuously weights the singular values as a function of β parameter. The choice of β is, in turn, the choice of a threshold on the acceptable singular values [31].…”

Sound source identification in a noisy environment based on inverse patch transfer functions with evanescent Green's functions

“…One main problem of regularization is the selection of breakpoints of the filter factors. Gauthier et al [39] defined the filter factors and adjust the regularization amount by using signal-to-noise ratio in acoustical inverse problems.…”