Optimal regularization and resolution limits for the reconstruction of acoustic source strength by inverse methods

Abstract

Generalized cross validation (GCV) provides an effective method for the determination of optimal regularization parameters in acoustical inverse problems. The problem of reconstructing acoustic source distributions from field measurements is very often ill-posed.The use of Tikonhov regularization, for example, often suppresses the effect of small singular values in the Green function matrix to be inverted and these are in turn often associated with ‘‘high spatial frequencies’’ of the source distribution. The net effect is to produce a useful estimate of the acoustic source strength distribution but with a limited spatial resolution. This paper will explore the relationship between estimation accuracy, spatial resolution, noise level, and source sensor geometry when a range of inverse sound radiation problems is regularized using GCV. [Youngtae Kim is supported by a British Council Grant which is gratefully acknowledged.]