Psychoacoustically motivated, frequency dependent Tikhonov regularization for soundfield parametrization

Noise is inevitably introduced during model based parametrization of acoustic fields, acquired using microphone arrays. This is due to the finite number of microphones used, the finite set of parameters used, modelling errors and errors due to non-ideal conditions such as transducer noise and positioning. The problem often manifests itself as an ill-posed matrix inversion that is accounted for by a regularization process. This has been studied extensively and often optimised for certain types of sources and transducers but never from the perspective of human perception. This lack of explicit psychoacoustic considerations is conspicuous especially if the parametrization is for subsequent immersive reproduction (as opposed to other applications such as localisation or beamforming). In this paper we use a novel approach that allows the trade-off of regularization noise, in terms of spatial and temporal resolution, as a function of frequency - thus allowing for psychoacoustic optimisation.