Differential fast fixed-point algorithms for underdetermined instantaneous and convolutive partial blind source separation

This paper concerns underdetermined linear instantaneous and convolutive blind source separation (BSS), i.e., the case when the number of observed mixed signals is lower than the number of sources.We propose partial BSS methods, which separate supposedly nonstationary sources of interest (while keeping residual components for the other, supposedly stationary, "noise" sources). These methods are based on the general differential BSS concept that we introduced before. In the instantaneous case, the approach proposed in this paper consists of a differential extension of the FastICA method (which does not apply to underdetermined mixtures). In the convolutive case, we extend our recent time-domain fast fixed-point C-FICA algorithm to underdetermined mixtures. Both proposed approaches thus keep the attractive features of the FastICA and C-FICA methods. Our approaches are based on differential sphering processes, followed by the optimization of the differential nonnormalized kurtosis that we introduce in this paper. Experimental tests show that these differential algorithms are much more robust to noise sources than the standard FastICA and C-FICA algorithms.Comment: this paper describes our differential FastICA-like algorithms for linear instantaneous and convolutive underdetermined mixture

Temporal and time-frequency correlation-based blind source separation methods. Part I : Determined and underdetermined linear instantaneous mixtures

We propose two types of correlation-based blind source separation (BSS) methods, i.e. a time-domain approach and extensions which use time-frequency (TF) signal representations and thus apply to much more general conditions. Our basic TF methods only require each source to be isolated in a tiny TF area, 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 (scaled permuted) mixing matrix in TF areas where these methods detect that a source is isolated. Both the detection and identification stages of these approaches use local correlation parameters of the TF transforms of the observed signals. Two such Linear Instantaneous TIme-Frequency CORRelation-based BSS methods are proposed, using Centered or Non-Centered TF transforms. These methods, which are resp. called LI-TIFCORR-C and LI-TIFCORR-NC, are especially suited to non-stationary sources. We derive their performance from many tests performed with mixtures of speech signals. This demonstrates that their output SIRs have a low sensitivity to the values of their TF parameters and are quite high, i.e. typically 60 to 80 dB, while the SIRs of all tested classical methods range about from 0 to 40 dB. We also extend these approaches to achieve partial BSS for underdetermined mixtures and to operate when some sources are not isolated in any TF area

Convolutive Blind Source Separation Methods

In this chapter, we provide an overview of existing algorithms for blind source separation of convolutive audio mixtures. We provide a taxonomy, wherein many of the existing algorithms can be organized, and we present published results from those algorithms that have been applied to real-world audio separation tasks