Wavenumber domain regularisation for near-field acoustic holography by means of modified filter functions and a cut-off and slope iteration

Planar Near-field Acoustic Holography (PNAH) is an acoustic imaging method based on the inverse solution of the wave equation. Wavenumber domain low-pass filtering is an essential operation in the PNAH process. An increasingly higher wavenumber filter cut-off results in a "blow-up" of the inverse solution, which is a characteristic of an ill-posed problem. On the other hand, lower cut-off wavenumbers result in spatial acoustic data at very low resolution, where highly detailed information is discarded. Thus, an optimal solution for the cut-off wavenumber somewhere in between is needed. This paper introduces two modified filter functions, namely a modified exponential and a modified Tikhonov filter, that are specifically designed for application in PNAH and compares them with a number of more general applied filter functions. Regularization methods are introduced that exploit the k-space to obtain near-optimal low-pass filter parameter selection at high computational efficiency. These filter functions are discussed and their parameters are selected by k-space application of L-curve, Generalised Cross-Validation and the newly introduced and well-applicable Cut-Off and Slope iteration. Simulations of various sources show that the optimal regularization method is highly dependent on the type of source, the spatial distribution and measurement noise. Finally, a robust regularization strategy is proposed which automatically produces high quality results for a wide range of practical conditions.