Dereverbering speech and cancelling additive noise as an errors-in-variables interpolation issue

In addition to measurement noise, echoes and reverberations may disturb speech recorded by a microphone. To describe the spatial transformation between the sources and the microphones, FIR filters are considered when modelling the system. Therefore, speech is contaminated by both convolutive and additive noises. In this paper, we propose to retrieve the speech signal from the noisy observations by using two microphones. This speech enhancement method operates in two steps. Firstly, the blind estimations of the FIRs are based on the non negative definiteness property of the autocorrelation matrix of the reverberated versions of speech. The estimation of the original speech is then viewed as an errors-in-variables interpolation issue. It should be noted that this method first deals with a white background noise and has the advantage of not using a voice activity detector (VAD), which is usually required to estimate the noise variances.