Binaural noise reduction based on widely linear filtering with multiple microphones

This paper deals with the problem of binaural noise reduction where there are multiple input channels and two output channels. The basic problem is to process the noisy signals observed by an array of microphones to produce two (binaural) outputs. On the one hand, the two outputs are expected to be much less noisy than the input signals and, on the other hand, the spatial information of the desired sound source should be preserved so that, after noise reduction, the listener will still be able to correctly localize the sound sources from the two outputs using his/her binaural hearing mechanism. To achieve this goal, we first combine the multiple real input signals into a number of complex signals. We also merge the two expected real outputs into a complex signal. By doing so, the original problem is converted into one of complex multiple-input/single-output noise reduction. The widely linear (WL) estimation theory is then used to derive optimal filters that can achieve noise reduction while preserving the desired speech signal and its spatial information. With this WL framework, the WL Wiener, WL minimum variance distortionless response (MVDR), and WL tradeoff filters are derived. We also discuss a WL linearly constrained minimum variance (LCMV) filter that can achieve noise reduction while preserving the spatial information of both the speech and noise sources.