Time-frequency ratio-based blind separation methods for attenuated and time-delayed sources

We propose two types of time-frequency (TF) blind source separation (BSS) methods suited to attenuated and delayed (AD) mixtures. These approaches, inspired from a method that we previously developed for linear instantaneous (LI) mixtures, almost only require each source to occur alone in a tiny TF zone, i.e. they set very limited constraints on the source sparsity and overlap, unlike various previously reported TF-BSS methods. Our approaches consist in identifying the columns of the (filtered permuted) mixing matrix in TF zones where these methods detect that a single source occurs, using TIme-Frequency Ratios Of Mixtures (hence their name TIFROM). We thus identify columns of scale coefficients and time shifts. The detection stage for time shifts uses regression lines associated to the above-mentioned TF ratios of mixtures. The detection stage for scale coefficients uses the variance of these TF ratios of mixtures, either in Constant-Time or in Constant-Frequency analysis zones. This yields two alternative BSS methods, which are resp. called AD-TIFROM-CT and AD-TIFROM-CF. These methods are especially suited to non-stationary sources. We derive their performance from many tests performed with AD mixtures of speech signals. This demonstrates that they yield major SNR improvements, i.e. about 45 dB with optimum parameters for time shifts ranging from 0 to 20 samples and above 18 dB for 200-sample time shifts.