Measuring Dependence for Permutation Alignment in Convolutive Blind Source Separation

This brief proposes an effective implementation for addressing permutation ambiguity issue of convolutive blind source separation in frequency domain. Generally, signal envelope and power ratio as common inter-frequency dependence measures are utilized to group bin-wise separated signals for convolutive mixtures, where the new measure of permutation alignment method is represented by the activation matrix of bin-wise spectrum which is based on nonnegative matrix factorization (NMF). Meanwhile, canonical correlation analysis (CCA) rather than the maximum sum of correlation coefficient among different bins, is applied for verifying correlation determinations. In addition, the influence of bin distance and separation quality at each bin are explored to optimize permutation result. Simulation results demonstrate the effectiveness of the proposed technique in real recorded convolutive mixtures.

I. Introduction

The purpose blind source separation (BSS) is to calculate the sources only on the basis of the observed mixtures without signal prior information and channel transmission system [1]. Convolutive BSS is a challenging topic since multiple sources and their unknown delayed versions are mixed simultaneously [2]–[4]. Meanwhile, frequency-domain approach is one of the most widespread convolutive BSS method, in which convolutive mixtures is first converted into the frequency-domain via short-time Fourier transform (STFT), afterwards the convolutive BSS can efficiently switch to a series of complex instantaneous BSS issues [5]. Although desired result of instantaneous separation can be achieved at each bin, integrating all bins to restructure original sources is a formidable task because there exist the ambiguity problem of permutation and scaling associated with individual bin [6]. It is well known that the measure selection plays a key role in signal similarity determination. Conventionally, envelopes [7] and power ratio [8]–[10] are widely used measures which achieve a good permutation alignment performance between adjacent bins with the maximization of correlation coefficients sum. Additionally, [11] utilizes the distance measure of information theory for solving the permutation problem, [12] illustrates the interaction between joint-block diagonalization and tensor decomposition to address the topic of permutation. Meanwhile, independent vector analysis (IVA) [13] is introduced to solve the permutation issue by introducing the vector source model. After that, independent low-rank matrix analysis (ILRMA) [14] is an ordinary speech separation technique, which unifies IVA and nonnegative matrix factorization (NMF) to make the low-rank signal model with time-frequency scheme instead of the vector version signal model applied in IVA. However, it is very difficult to find an universal source model that works for all kinds of sound sources. Thus the strategy of permutation is very important for bin-wise convolutive mixtures.