Design of an optimal wave-vector filter for enhancing the resolution of reconstructed source field by near-field acoustical holography (NAH)

Abstract

In near-field acoustical holography using the boundary element method, the reconstructed field often diverges due to the presence of small measurement errors. In order to handle this instability in the inverse problem, the reconstruction process should include some form of regularization for enhancing the resolution of source images. The usual method of regularization has been the truncation of wave vectors associated with small singular values, although the determination of an optimal truncation order is difficult. In this article, an iterative inverse solution technique is suggested in which the mean-square error prediction is used. A statistical estimation of the minimum mean-square error between measured pressures and the model solution is required for yielding the optimal number of iterations. The continuous curve of an optimal wave-vector filter is designed, for suppressing the high-order modes that can produce large reconstruction errors. Experimental results from a baffled radiator reveal that the reconstruction errors can be reduced by this form of regularization, by at least 48% compared to those without any regularization. In comparison to results using the optimal truncation method of regularization, the new scheme is shown to give further reductions of truncation error of between 7% and 39%, for the example in this article. (C) 2000 Acoustical Society of America. [S0001-4966(00)04006-6].