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Wavenumber Domain Regularization for Near-Field Acoustic Holography by Means of Modified Filter Functions and Cut-Off and Slope Iteration

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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.

Document Type: Research Article

DOI: http://dx.doi.org/10.3813/AAA.918041

Publication date: May 1, 2008

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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