Energetically optimal regularization in nearfield acoustical holography

Abstract

Regularization techniques, such as singular value discarding or Tikhonov regularization, are commonly used to improve estimate of source field to be reconstructed from measured acoustic pressures at many points in nearfield acoustical holography. Theoretically, however, the regularized solution always underestimates the sound power of the real source. This paper presents an energetically optimal regularization method to solve this problem in nearfield acoustical holography by introducing a compensation factor in the generalized cross-validation function used to determine the optimal regularization parameter based on the Tikhonov regularization technique. Numerical examples show that the resulting regularization parameter will not only ensure a good fit of the predicted acoustic pressures to all measured data, but also ensure that the sound power of the equivalent source is always in agreement with the measured sound power, thus making this regularization method more ideal and much better than others in finding a compromise between the fidelity to input data and the fidelity to source field, and yielding a robust solution to the source field. [Work supported by NSF.]