Binaural noise reduction in the time domain with a stereo setup

Binaural noise reduction with a stereophonic (or simply stereo) setup has become a very important problem as stereo sound systems and devices are being more and more deployed in modern voice communications. This problem is very challenging since it requires not only the reduction of the noise at the stereo inputs, but also the preservation of the spatial information embodied in the two channels so that after noise reduction the listener can still localize the sound source from the binaural outputs. As a result, simply applying a traditional single-channel noise reduction technique to each channel individually may not work as the spatial effects may be destroyed. In this paper, we present a new formulation of the binaural noise reduction problem in stereo systems. We first form a complex signal from the stereo inputs with one channel being its real part and the other being its imaginary part. By doing so, the binaural noise reduction problem can be processed by a single-channel widely linear filter. The widely linear estimation theory is then used to derive optimal noise reduction filters that can fully take advantage of the noncircularity of the complex speech signal to achieve noise reduction while preserving the desired signal (speech) and spatial information. With this new formulation, the Wiener, minimum variance distortionless response (MVDR), maximum signal-to-noise ratio (SNR), and tradeoff filters are derived. Experiments are provided to justify the effectiveness of these filters.