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

Abstract

Tikhonov regularization method is effective in stabilizing reconstruction process of the near-field acoustic holography (NAH) based on the equivalent source method (ESM), and the selection of the optimal regularization parameter is a key problem that determines the regularization effect. In this work, a new method for determining the optimal regularization parameter is proposed. The transfer matrix relating the source strengths of the equivalent sources to the measured pressures on the hologram surface is augmented by adding a fictitious point source with zero strength. The minimization of the norm of this fictitious point source strength is as the criterion for choosing the optimal regularization parameter since the reconstructed value should tend to zero. The original inverse problem in calculating the source strengths is converted into a univariate optimization problem which is solved by a onedimensional search technique. Two numerical simulations with a point driven simply supported plate and a pulsating sphere are investigated to validate the performance of the proposed method by comparison with the L-curve method. The results demonstrate that the proposed method can determine the regularization parameter correctly and effectively for the reconstruction in NAH.

A Forward−Backward Splitting Equivalent Source Method Based on S−Difference

“…When using this method, the regularization parameter needs to be determined first, and the reconstruction result depends heavily on the accurate selection of the regularization parameter. The commonly used regularization parameter selection methods mainly include the L−curve method and Generalized Cross Validation (GCV) [8,9]. In recent years, compressed sensing technology based on sparse regularization has been widely used in the field of image processing [10,11].…”