A multichannel widely linear approach to binaural noise reduction using an array of microphones

This paper deals with the problem of binaural noise reduction using an array of microphones. This is a very important problem in applications such as teleconferencing and hearing aids where there is a need to mitigate the noise effect from the noisy signals picked up by multiple microphones and produce two "clean" outputs. The mitigation of the noise should be made in such a way that no audible distortion is added to the two outputs (this is the same as in the single-channel case) and meanwhile the spatial information of the desired sound source should be preserved so that, after noise reduction, the listener will still be able to localize the sound source thanks to his/her binaural hearing mechanism. In this paper, we present a novel approach to this problem where we first form a number of complex input signals from the multiple and real microphone observations. We also merge the two expected real outputs into a complex output signal. The widely linear estimation theory is then used to derive optimal noise reduction filters that can achieve noise reduction while preserving the desired signal (speech) and its spatial information. With this new formulation, the Wiener and minimum variance distortionless response (MVDR) filters are derived. Experiments are provided to justify the effectiveness of these filters.