Shoko Araki

A robust and precise method for solving the permutation problem of frequency-domain blind source separation

Blind source separation (BSS) for convolutive mixtures can be solved efficiently in the frequency domain, where independent component analysis (ICA) is performed separately in each frequency bin. However, frequency-domain BSS involves a permutation problem: the permutation ambiguity of ICA in each frequency bin should be aligned so that a separated signal in the time-domain contains frequency components of the same source signal. This paper presents a robust and precise method for solving the permutation problem. It is based on two approaches: direction of arrival (DOA) estimation for sources and the interfrequency correlation of signal envelopes. We discuss the advantages and disadvantages of the two approaches, and integrate them to exploit their respective advantages. Furthermore, by utilizing the harmonics of signals, we make the new method robust even for low frequencies where DOA estimation is inaccurate. We also present a new closed-form formula for estimating DOAs from a separation matrix obtained by ICA. Experimental results show that our method provided an almost perfect solution to the permutation problem for a case where two sources were mixed in a room whose reverberation time was 300 ms.

The fundamental limitation of frequency domain blind source separation for convolutive mixtures of speech

Despite several recent proposals to achieve blind source separation (BSS) for realistic acoustic signals, the separation performance is still not good enough. In particular, when the impulse responses are long, performance is highly limited. In this paper, we consider a two-input, two-output convolutive BSS problem. First, we show that it is not good to be constrained by the condition T>P, where T is the frame length of the DFT and P is the length of the room impulse responses. We show that there is an optimum frame size that is determined by the trade-off between maintaining the number of samples in each frequency bin to estimate statistics and covering the whole reverberation. We also clarify the reason for the poor performance of BSS in long reverberant environments, highlighting that the framework of BSS works as two sets of frequency-domain adaptive beamformers. Although BSS can reduce reverberant sounds to some extent like adaptive beamformers, they mainly remove the sounds from the jammer direction. This is the reason for the difficulty of BSS in reverberant environments.

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

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.

Underdetermined blind sparse source separation for arbitrarily arranged multiple sensors

This paper presents a new method for blind sparse source separation. Some sparse source separation methods, which rely on source sparseness and an anechoic mixing model, have already been proposed. These methods utilize level ratios and phase differences between sensor observations as their features, and they separate signals by classifying them. However, some of the features cannot form clusters with a well-known clustering algorithm, e.g., the k-means. Moreover, most previous methods utilize a linear sensor array (or only two sensors), and therefore they cannot separate symmetrically positioned sources. To overcome such problems, we propose a new feature that can be clustered by the k-means algorithm and that can be easily applied to more than three sensors arranged non-linearly. We have obtained promising results for two- and three-dimensionally distributed speech separation with non-linear/non-uniform sensor arrays in a real room even in underdetermined situations. We also investigate the way in which the performance of such methods is affected by room reverberation, which may cause the sparseness and anechoic assumptions to collapse.

Grouping Separated Frequency Components by Estimating Propagation Model Parameters in Frequency-Domain Blind Source Separation

This paper proposes a new formulation and optimization procedure for grouping frequency components in frequency-domain blind source separation (BSS). We adopt two separation techniques, independent component analysis (ICA) and time-frequency (T-F) masking, for the frequency-domain BSS. With ICA, grouping the frequency components corresponds to aligning the permutation ambiguity of the ICA solution in each frequency bin. With T-F masking, grouping the frequency components corresponds to classifying sensor observations in the time-frequency domain for individual sources. The grouping procedure is based on estimating anechoic propagation model parameters by analyzing ICA results or sensor observations. More specifically, the time delays of arrival and attenuations from a source to all sensors are estimated for each source. The focus of this paper includes the applicability of the proposed procedure for a situation with wide sensor spacing where spatial aliasing may occur. Experimental results show that the proposed procedure effectively separates two or three sources with several sensor configurations in a real room, as long as the room reverberation is moderately low.

Measuring Dependence of Bin-wise Separated Signals for Permutation Alignment in Frequency-domain BSS

This paper presents a new method for grouping bin-wise separated signals for individual sources, i.e., solving the permutation problem, in the process of frequency-domain blind source separation. Conventionally, the correlation coefficient of separated signal envelopes is calculated to judge whether or not the separated signals originate from the same source. In this paper, we propose a new measure that represents the dominance of the separated signal in the mixtures, and use it for calculating the correlation coefficient, instead of a signal envelope. Such dominance measures exhibit dependence/independence more clearly than traditionally used signal envelopes. Consequently, a simple clustering algorithm with centroids works well for grouping separated signals. Experimental results were very appealing, as three sources including two coming from the same direction were separated properly with the new method.

The 2008 Signal Separation Evaluation Campaign: A Community-Based Approach to Large-Scale Evaluation

This paper introduces the first community-based Signal Separation Evaluation Campaign (SiSEC 2008), coordinated by the authors. This initiative aims to evaluate source separation systems following specifications agreed between the entrants. Four speech and music datasets were contributed, including synthetic mixtures as well as microphone recordings and professional mixtures. The source separation problem was split into four tasks, each evaluated via different objective performance criteria. We provide an overview of these datasets, tasks and criteria, summarize the results achieved by the submitted systems and discuss organization strategies for future campaigns.

Blind Extraction of Dominant Target Sources Using ICA and Time-Frequency Masking

This paper presents a method for enhancing target sources of interest and suppressing other interference sources. The target sources are assumed to be close to sensors, to have dominant powers at these sensors, and to have non-Gaussianity. The enhancement is performed blindly, i.e., without knowing the position and active time of each source. We consider a general case where the total number of sources is larger than the number of sensors, and neither the number of target sources nor the total number of sources is known. The method is based on a two-stage process where independent component analysis (ICA) is first employed in each frequency bin and then time-frequency masking is used to improve the performance further. We propose a new sophisticated method for deciding the number of target sources and then selecting their frequency components. We also propose a new criterion for specifying time-frequency masks. Experimental results for simulated cocktail party situations in a room, whose reverberation time was 130 ms, are presented to show the effectiveness and characteristics of the proposed method

Equivalence between frequency-domain blind source separation and frequency-domain adaptive beamforming for convolutive mixtures

Frequency-domain blind source separation (BSS) is shown to be equivalent to two sets of frequency-domain adaptive beamformers (ABFs) under certain conditions. The zero search of the off-diagonal components in the BSS update equation can be viewed as the minimization of the mean square error in the ABFs. The unmixing matrix of the BSS and the filter coefficients of the ABFs converge to the same solution if the two source signals are ideally independent. If they are dependent, this results in a bias for the correct unmixing filter coefficients. Therefore, the performance of the BSS is limited to that of the ABF if the ABF can use exact geometric information. This understanding gives an interpretation of BSS from a physical point of view.

Multichannel Extensions of Non-Negative Matrix Factorization With Complex-Valued Data

This paper presents new formulations and algorithms for multichannel extensions of non-negative matrix factorization (NMF). The formulations employ Hermitian positive semidefinite matrices to represent a multichannel version of non-negative elements. Multichannel Euclidean distance and multichannel Itakura-Saito (IS) divergence are defined based on appropriate statistical models utilizing multivariate complex Gaussian distributions. To minimize this distance/divergence, efficient optimization algorithms in the form of multiplicative updates are derived by using properly designed auxiliary functions. Two methods are proposed for clustering NMF bases according to the estimated spatial property. Convolutive blind source separation (BSS) is performed by the multichannel extensions of NMF with the clustering mechanism. Experimental results show that 1) the derived multiplicative update rules exhibited good convergence behavior, and 2) BSS tasks for several music sources with two microphones and three instrumental parts were evaluated successfully.