Patch near-field acoustic holography: Regularized extension and statistically optimized methods

The patch holography method allows one to make measurements on an extended structure using a small microphone array. Increased attention has been paid to the two techniques, which are quite different at first glance. One is to extrapolate the pressure field measured on the hologram plane while the other is to use statistically optimized processing. A singular value decomposition formulation of the latter is proposed in this paper. The similarity of the two techniques is shown here. Both use a convolution of the measured pressure patch to obtain a better estimate of the wavenumber spectrum backward propagated on the structure. By using the Morozov discrepancy principle to compute the regularization parameter, the two methods lead to very close results.