Mitsuru Kawamoto

A neural net for blind separation of nonstationary signals

Abstract This paper proposes a neural network that recovers some original random signals from their linear mixtures observed by the same number of sensors. The network acquires the function with a learning process without using any particular information about the statistical properties of the sources and the coefficients of the linear transformation, except the fact that the source signals are statistically independent and nonstationary. The learning rule for the networks parameters is derived from the steepest descent minimization of a time-dependent cost function that takes the minimum only when the network outputs are uncorrelated with each other.

A method of blind separation for convolved non-stationary signals

Abstract This paper proposes a method of “blind separation” which extracts non-stationary signals (e.g., speech signals, music) from their convolutive mixtures (observed signals). The function is acquired by modifying a networks parameters so that a cost function takes the minimum at any time. The cost function is the one introduced by Matsuoka et al. (Neural Networks 8 (3) (1995) 411–419). The learning rule is derived from the natural gradient (Amari et al., 1998, IEEE Trans. Signal Processing, submitted) minimization of the cost function. The validity of the proposed method is confirmed by computer simulation. The proposed method is applied to the case of No (the number of observed signals)=Ns (the number of source signals) and No>Ns.

A neural network that self-organizes to perform three operations related to principal component analysis

Abstract The self-organization of a linear, single-layer neural network is mathematically analyzed, in which a regular Hebbian rule and an anti-Hebbian rule are used for the adaptation of the connection weights between constituent units. It is shown that three mathematical functions related to principal component analysis are acquired by giving three different sets of learning parameters to the same model.

Eigenvector Algorithms Incorporated With Reference Systems for Solving Blind Deconvolution of MIMO-IIR Linear Systems

This letter presents an eigenvector algorithm (EVA) for blind deconvolution (BD) of multiple-input multiple-output infinite impulse response (MIMO-IIR) channels (convolutive mixtures), using the idea of reference signals. Differently from the conventional researches on EVAs, the proposed EVA utilizes only one reference signal for recovering all the source signals simultaneously. Computer simulations are presented for demonstrating the effectiveness of the proposed algorithm.

Adaptive super-exponential algorithms for blind deconvolution of MIMO systems

Multichannel blind deconvolution of finite-impulse response (FIR) or infinite-impulse response (IIR) systems is investigated using the multichannel super-exponential method. First, some properties are shown for the rank of the correlation matrices relevant to the multichannel super-exponential method. Then, the matrix inversion lemma is extended to the degenerate rank case. Based on these results, two types of adaptive multichannel super-exponential algorithms are presented, that is, the one in covariance form and the other in QR-factorization form.

A Matrix Pseudo-Inversion Lemma and Its Application to Block-Based Adaptive Blind Deconvolution for MIMO Systems

The matrix inversion lemma gives an explicit formula of the inverse of a positive-definite matrix A added to a block of dyads (represented as BBH) as follows: (A + BB^H)^-1 = A^-1 - A^-1 B(I + B^H A^-1 B) ^-1 B^H A^-1. It is well-known in the literature that this formula is very useful to develop a block-based recursive least-squares algorithm for the block-based recursive identification of linear systems or the design of adaptive filters. We extend this result to the case when the matrix A is singular, and present a matrix pseudo-inversion lemma. Based on this result, we propose a block-based adaptive multi-channel super-exponential algorithm (BAMSEA). We present simulation results for the performance of the block-based algorithm in order to show the usefulness of the matrix pseudo-inversion lemma.

Super-exponential Methods Incorporated with Higher-Order Correlations for Deflationary Blind Equalization of MIMO Linear Systems

The multichannel blind deconvolution of finite-impulse response (FIR) or infinite-impulse response (IIR) systems is investigated using the multichannel super-exponential deflation methods. In the conventional multichannel super-exponential deflation method [4], the so-called “second-order correlation method” is incorporated in order to estimate the contributions of an extracted source signal to the channel outputs. We propose a new multichannel super-exponential deflation method using higher-order correlations instead of second-order correlations to reduce the computational complexity in terms of multiplications and to accelerate the performance of equalization. By computer simulations, it is shown that the method of using fourth-order correlations is better than the method of using second-order correlations in a noiseless case or a noisy case.

A neural net for blind separation of nonstationary signal sources

This paper proposes a neural network that learns to recover the original random signals from their linear mixtures observed by the same number of sensors. The network acquires the function without using any information about the statistical properties of the sources and the coefficients of the linear transformation, except the assumption that the source signals are statistically independent and nonstationary. The learning rule is formulated as a steepest descent minimization of a time-dependent cost function that takes the minimum only when the network outputs are uncorrelated with each other.<<ETX>>

A Matrix Pseudoinversion Lemma and Its Application to Block-Based Adaptive Blind Deconvolution for MIMO Systems

The matrix inversion lemma gives an explicit formula of the inverse of a positive definite matrix <i>A</i> added to a block of dyads (represented as <i>BB</i>^H) as follows: (<i>A</i>+<i>BB</i>^H)^-1= <i>A</i>^-1- <i>A</i>^-1<i>B</i>(<i>I</i> + <i>B</i>^H<i>A</i>^-1<i>B</i>)^-1<i>B</i>^H<i>A</i>^-1. It is well known in the literature that this formula is very useful to develop a block-based recursive least squares algorithm for the block-based recursive identification of linear systems or the design of adaptive filters. We extend this result to the case when the matrix <i>A</i> is singular and present a matrix pseudoinversion lemma along with some illustrative examples. Based on this result, we propose a block-based adaptive multichannel superexponential algorithm. We present simulation results for the performance of the block-based algorithm in order to show the usefulness of the matrix pseudoinversion lemma.

Tracking Intermittently Speaking Multiple Speakers Using a Particle Filter

The problem of tracking multiple intermittently speaking speakers is difficult as some distinct problems must be addressed. The number of active speakers must be estimated, these active speakers must be identified, and the locations of all speakers including inactive speakers must be tracked. In this paper we propose a method for tracking intermittently speaking multiple speakers using a particle filter. In the proposed algorithm the number of active speakers is firstly estimated based on the Exponential Fitting Test (EFT), a source number estimation technique which we have proposed. The locations of the speakers are then tracked using a particle filtering framework within which the decomposed likelihood is used in order to decouple the observed audio signal and associate each element of the decomposed signal with an active speaker. The tracking accuracy is then further improved by the inclusion of a silence region detection step and estimation of the noise-only covariance matrix. The method was evaluated using live recordings of 3 speakers and the results show that the method produces highly accurate tracking results.