A multichannel widely linearwiener filter for binaural noise reduction in the short-time-fourier-transform domain

Binaural noise reduction is a very challenging problem since it requires not only to reduce noise, but also to recover the spatial information of the desired speech source so that the listener can localize this source from the binaural outputs. In this paper, we study the problem in the short-time-Fourier-transform (STFT) domain with the use of an array of microphones. Combining the multichannel microphone observations into a number of complex signals and merging the two (binaural) expected output channels into a complex signal, we reformulate the problem with the widely linear (WL) estimation technique. To efficiently achieve the optimal estimation, the complex signals are transformed into the frequency domain via the STFT. We then derive a WL Wiener filter based on the WL estimation theory and the mean-squared-error (MSE) criterion. This WL Wiener filter is shown to be able to exploit the noncircularity of the complex speech signals and the spatial information captured by the microphone array to achieve noise reduction while preserving the sound spatial information.