Binary time-frequency masks are powerful tools for the separation of sources from a single mixture. Perfect demixing via binary time-frequency masks is possible provided the time-frequency representations of the sources do not overlap: a condition we call W-disjoint orthogonality. We introduce here the concept of approximate W-disjoint orthogonality and present experimental results demonstrating the level of approximate W-disjoint orthogonality of speech in mixtures of various orders. The results demonstrate that there exist ideal binary time-frequency masks that can separate several speech signals from one mixture. While determining these masks blindly from just one mixture is an open problem, we show that we can approximate the ideal masks in the case where two anechoic mixtures are provided. Motivated by the maximum likelihood mixing parameter estimators, we define a power weighted two-dimensional (2-D) histogram constructed from the ratio of the time-frequency representations of the mixtures that is shown to have one peak for each source with peak location corresponding to the relative attenuation and delay mixing parameters. The histogram is used to create time-frequency masks that partition one of the mixtures into the original sources. Experimental results on speech mixtures verify the technique. Example demixing results can be found online at http://alum.mit.edu/www/rickard/bss.html.

Blind separation of speech mixtures via time-frequency masking

This paper presents a blind source separation method for convolutive mixtures of speech/audio sources. The method can even be applied to an underdetermined case where there are fewer microphones than sources. The separation operation is performed in the frequency domain and consists of two stages. In the first stage, frequency-domain mixture samples are clustered into each source by an expectation-maximization (EM) algorithm. Since the clustering is performed in a frequency bin-wise manner, the permutation ambiguities of the bin-wise clustered samples should be aligned. This is solved in the second stage by using the probability on how likely each sample belongs to the assigned class. This two-stage structure makes it possible to attain a good separation even under reverberant conditions. Experimental results for separating four speech signals with three microphones under reverberant conditions show the superiority of the new method over existing methods. We also report separation results for a benchmark data set and live recordings of speech mixtures.

/pdf/underdetermined-convolutive-blind-source-separation-via-274tgvo8m6.pdf

Underdetermined Convolutive Blind Source Separation via Frequency Bin-Wise Clustering and Permutation Alignment

A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources

http://www.tara.tsukuba.ac.jp/~maki/reprint/Araki/sa07sp1833-1847.pdf

Underdetermined blind sparse source separation for arbitrarily arranged multiple sensors

Source separation arises in a variety of signal process- ing applications, ranging from speech processing to medical image analysis. The separation of a superposition of multiple signals is accomplished by taking into account the structure of the mixing proc- ess and by making assumptions about the sources. When the infor- mation about the mixing process and sources is limited, the problem is called ''blind'. By assuming that the sources can be represented sparsely in a given basis, recent research has demonstrated that sol- utions to previously problematic blind source separation problems can be obtained. In some cases, solutions are possible to problems intractable by previous non-sparse methods. Indeed, sparse meth-

/pdf/survey-of-sparse-and-non-sparse-methods-in-source-separation-4ow78wdark.pdf

Survey of sparse and non-sparse methods in source separation

We have developed a method of segregating desired speech from concurrent sounds received by two microphones. In this method, which we call SAFIA, signals received by two microphones are analyzed by discrete Fourier transformation. For each frequency component, differences in the amplitude and phase between channels are calculated. These differences are used to select frequency components of the signal that come from the desired direction and to reconstruct these components as the desired source signal. To clarify the effect of frequency resolution on the proposed method, we conducted three experiments. First, we analyzed the relationship between frequency resolition and the power spectrum’s cumulative distribution. We found that the speech-signal power was concentrated on specific frequency components when the frequency resolution was about 10-Hz. Second, we determined whether a given frequency resolution decreased the overlap between the frequency components of two speech signals. A 10-Hz frequency resolution minimized the overlap. Third, we analyzed the relationship between sound quality and frequency resolution through subjective tests. The best frequency resolution in terms of sound quality corresponded to the frequency resolutions that concentrated the speech signal power on specific frequency components and that minimized the degree of overlap. Finally, we demonstrated that this method improved the signal-to-noise ratio by over 18dB.

Tetsuma Sakurai

Papers

Sound source segregation based on estimating incident angle of each frequency component of input signals acquired by multiple microphones