Masashi Ohata

Stability analyses of information-theoretic blind separation algorithms in the case where the sources are nonlinear processes

A basic approach to blind source separation is to define an index representing the statistical dependency among the output signals of the separator and minimize it with respect to the separators parameters. The most natural index might be mutual information among the output signals of the separator. In the case of a convolutive mixture, however, since the signals must be treated as a time series, it becomes very complicated to concretely express the mutual information as a function of the parameters. To cope with this difficulty, in most of the conventional methods, the source signals are assumed to be independent identically distributed (i.i.d.) or linear. Based on this assumption, some simpler indices are defined, and their minimization is made by such an iterative calculation as the gradient method. In actual applications, however, the sources are often not linear processes. This paper discusses what will happen when those algorithms postulating the linearity of the sources are applied to the case of nonlinear sources. An analysis of local stability derives a couple of conditions guaranteeing that the separator stably tends toward a desired one with iteration. The obtained results reveal that those methods, which are based on the minimization of some indices related to the mutual information, do not work well when the sources signals are far from linear.

An adaptive blind separation method using para-Hermitian whitening filter for convolutively mixed signals

In this paper, we propose an adaptive method for blind separation of convolutively mixed sources. The method is an extension on the basis of two-stage separation approach using fourth-order cumulant. As in the case of instantaneous mixtures, the algorithm is composed of two processes: prewhitening and separation. For prewhitening we employ a whitening filter that is optimal in a certain sense, but this means constraining the whitening matrix in the manifold of positive-definite, para-Hermitian matrices. The whitening filter is close to the identity matrix in the set of whitening filters. Accordingly, the length of whitening filter can be shortened. In addition, the number of iterative calculations required for a design of the filter can be small. For separation we need to constrain the separating filter in the manifold of para-unitary matrices. We describe how to implement these constraints in a complete time-domain, and the adaptive method. To demonstrate the effectiveness of our method, we performed computer simulations and experiments using measurements of speeches nixed in an actual environment.

A kurtosis-based blind separation of sources using the Cayley transform

This paper proposes a new kurtosis-based method for blind separation of sources. For instantaneous mixture of sources, the conventional kurtosis-based approaches provide an elegant solution, where separation is made by minimizing or maximizing certain contrast functions with respect to an orthogonal matrix representing the separator. In the case of a convolutive mixture, however the class of orthogonal matrices need to be extended to that of para-unitary matrices, and its treatment becomes cumbersome. In this paper the problem is overcome by introducing the Cayley transform, which transforms a para-unitary matrix to a para-skew-Hermitian matrix. The fact that the set of para-skew-Hermitian matrices is a vector space offers a relatively simple method for kurtosis-based blind separation of convolutively mixed signals.

An online algorithm for blind source separation with Gaussian mixture model

This paper proposes a new online algorithm for blind source separation. It is based on the maximum likelihood estimation of the mixing matrix and the parameterized probability density functions of the sources. For the model of each source signal a Gaussian mixture model is adopted. When one attempts to devise an online algorithm in this framework, two problems arise. First, what kind of recursive minimization is efficient from a computational point of view? Second, how can the singularity of the likelihood function associated with the mixture model be avoided? Same techniques for solving these problems are described.

Frequency-domain implementation of a time-domain blind separation algorithm for convolutive mixtures of sources

This paper proposes a way to implement a time-domain blind separation algorithm for convolutive mixtures of source signals. The approach provides another form of the algorithm by discrete Fourier transform and has the possibility of designing a separating filter in the frequency domain, without bothering about the permutation problem inherent in frequency-domain blind separation approach. This paper also shows a technique to improve separation performance in the frequency domain. The validity of our approach was demonstrated by performing an experiment on separation for convolutive mixtures of two speeches.

Blind separation of convolutive mixtures of speech signals using linear combination model

In this paper, we propose a blind separation algorithm for convolutive mixture of source signals on the basis of the information-theoretical approach. This approach requires distribution models of the sources. It is difficult to select the models without prior knowledge of sources. In order to resolve the difficulty, we introduce a distribution model with parameters. We construct the parametric model by linearly combining two density functions corresponding to sub- and super-Gaussian distributions. Our algorithm adaptively estimates the parameters and designs a separat- ing filter. We applied the algorithm to convolutive mix- tures of two speeches in a real environment. The result of our experiments shows that our algorithm can improve separation performance.

Blind separation with Gaussian mixture model for convolutively mixed sources

This paper proposes an online blind separation algorithm with Gaussian mixture model for convolutively mixed sources. Although similar algorithms were proposed, they were derived for independent and identically distributed (iid) sources. They may not work for sources which are not made iid by any linear filter. From the theoretical viewpoint, our algorithm also works well for the sources and search for an optimal separator simultaneously, it can be applied to the case where their statistical properties are quite unknown, except that sources are nonGaussian.

Adaptive Robust Super-exponential Algorithms for Deflationary Blind Equalization of Instantaneous Mixtures

The so called “super-exponential” algorithms (SEA’s) are attractive algorithms for solving blind signal processing problems. The conventional SEA’s, however, have such a drawback that they are very sensitive to Gaussian noise. To overcome this drawback, we propose a new SEA. While the conventional SEA’s use the second- and higher-order cumulants of observations, the proposed SEA uses only the higher-order cumulants of observations. Since higher-order cumulants are insensitive to Gaussian noise, the proposed SEA is robust to Gaussian noise, which is referred to as a robust super-exponential algorithm (RSEA). The proposed RSEA is implemented as an adaptive algorithm, which is referred to as an adaptive robust super-exponential algorithm (ARSEA). To show the validity of the ARSEA, some simulation results are presented.