A New Sparse Blind Source Separation Method for Determined Linear Convolutive Mixtures in Time-Frequency Domain

Abstract

This paper presents a new Blind Source Separation method for linear convolutive mixtures, which exploits the sparsity of source signals in the time-frequency domain. This method especially brings a solution to the artifacts problem that affects the quality of signals separated by existing time-frequency methods. These artifacts are in fact introduced by a time-frequency masking operation, used by all these methods. Indeed, by focusing on the case of determined mixtures, we show that this problem can be solved with much less restrictive sparsity assumptions than those of existing methods. Test results show the superiority of our new proposed method over existing ones based on time-frequency masking.

Multi-Channel Bin-Wise Speech Separation Combining Time-Frequency Masking and Beamforming

“…for M < N ) [5], [7], [14], the case of convolutive mixtures remains of interest in BSS research. These techniques can be split into two main categories: frequency-domain methods [1], [3], [7], [14], [15], which mainly handle mixtures in the time-frequency (TF) domain, and time-domain methods [6], [16], [17], which handle mixtures in the time domain.…”

“…As for the frequency-domain methods, they have shown their good performances even in the determined case (i.e. M = N ) or underdetermined case, and this despite the increasing reverberation time [3]- [5], [7], [14], [15], [18]- [26]. These frequency-domain methods begin by transposing Eq.…”

“…• X i (n, f ) and S j (n, f ) are respectively the STFT of x i (t) and s j (t); n represents the time dimension and f the frequency dimension, • K and T are respectively the length of the analysis window 3 and the number of time windows used by the STFT, • H ij (f ) is the discrete Fourier transform of h ij (t) computed on f points for source with index j.…”

“…However, these methods are not applicable in the case of underdetermined mixtures. For the underdetermined case, frequency domain BSS methods generally rely on a sparsity [3]- [5], [7], [14], [18]- [20], [23], [24] or a non-negativity [21], [22] assumption in the TF plane. Nonnegative Matrix Factorization (NMF) methods exploiting the non-negativity of the sources have shown their efficiency in several works [21], [22].…”

“…In various methods, channel features such as amplitude ratios and phase differences between frequency observations are computed at each TF bin. These features are then utilized to estimate TF masks using either clustering methods [1], [3], [7], [14], [29] or deep neural networks (DNN) [30]- [33]. It is worth noting that DNN-based methods typically require a large amount of training data, and their performance may significantly degrade if the training and test settings differ.…”