The determination of regularization parameters in planar nearfield acoustic holography

The reconstruction of Nearfield Acoustic Holography(NAH) is a linear,ill-posed inverse problem,in which a regularization procedure must be used.We compared three Tikhonov regularization based parameter selection methods, Morozov Discrepancy Principle method(MDP),Generalized Cross Validation method(GCV),and L-curve method,at various hologram distances,sound source frequencies,and Signal-to-Noise Ratios(SNR).The results show that they are all not robust at large hologram distances and low noise conditions.Based on an equivalent-noise-variance method,we established an improved method for estimating the noise variance in the MDP method,which is relative robust among the three,and made it work at relatively large hologram distances and low noise conditions.Numerical simulations show that the improved MDP method is robust in determining proper regularization parameters over a large SNR range(6 dB) and at a relatively large hologram distance(～10 cm).Moreover,the improved MDP method has a valid reconstruction aperture that is equal to the hologram aperture because it is not necessary to smooth the hologram pressure.