平面近场声全息中正则化参数的确定

近场声全息的逆向重建过程属于线性病态逆问题,必须进行正则化处理。本文对三种基于Tikhonov正则化的参数选择方法,即离差原理法、广义交叉验证法、L曲线法,在不同全息距离、声源频率和信噪比的条件下进行了比较,结果表明,它们在远距离及低噪声环境下难以获得合适的正则化参数。采用等效噪声方差的方法,对其中较为稳定的离差原理进行了改进,使其在较远全息距离及低噪声环境下仍能获得合适的正则化参数。相应的仿真实验表明,改进后的离差原理法在很宽的信噪比(6 dB)和较远的全息距离(～10 cm)均能稳定地找到合适的正则化参数。此外,由于该方法无须对全息声压进行平滑处理,其有效重建孔径和全息孔径相等。

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.