A study on regularization parameter choice in near-field acoustical holography

Regularization plays an important role in Near-field Acoustical Holography (NAH), and choosing the right amount of regularization is crucial in order to get a meaningful solution. An automated method such as the L-curve or Generalized Cross-Validation (GCV) is often used in NAH to choose a regularization parameter.

These parameter choice methods (PCMs) are attractive, since they require no a priori knowledge about the noise. However, there seems to be no clear understanding of when one PCM is better than the other. This paper presents comparisons of three PCMs: GCV, L-curve and Normalized Cumulative Periodogram (NCP).

The latter method is new within NAH and it is based on the Fourier transform of the residual vector. The methods are used in connection with three NAH methods: Statistically Optimized Near-field Acoustical Holography (SONAH), the Inverse Boundary Element Method (IBEM), and the Equivalent Source Method (ESM).

All combinations of the PCMs and the NAH methods are investigated using simulated measurements with different types of noise added to the input. Finally, the comparisons are carried out for a practical experiment. This aim of this work is to create a better understanding of which mechanisms that affect the performance of the different PCMs.