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Noisy speech dereverberation as a SIMO system identification issue

This paper deals with the speech dereverberation issue based on a single input multiple output (SIMO) system, when the reverberations are modeled by finite impulse response (FIR) filters. In most of the existing methods, the authors assume either that the white noises have the same variance or that the noise statistics are available. Here, we investigate the blind speech deconvolution using two microphones, when the white noise variances are not equal. For this purpose, we present a modified version of an identification approach previously developed in the framework of control and based on the properties of the definiteness and the positiveness of the autocorrelation matrices of the reverberated versions of the speech and the observations. This makes it possible to estimate both the variances of the additive noises and the FIR. Then, the speech signal is retrieved in the least square (LS) or minimum variance (MV) sense