Recently we have developed an eigenvector method (EVM) which can achieve the blind deconvolution (BD) for MIMO systems. The attractive features of the proposed algorithm are that the BD can be achieved by calculating the eigenvectors of a matrix and by using reference signals. However, the performance accuracy of the EVM depends highly on the computational result of the eigenvectors. In this paper, by modifying the EVM, we propose an algorithm which can achieve the BD without calculating the eigenvectors. Then the pseudo-inverse which is needed to carry out the BD is calculated by our proposed matrix pseudo-inversion lemma. Simulation results will be presented for showing the validity of the proposed method.

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). 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 already extended this result to the case when the matrix A is singular, and presented the matrix pseudo-inversion lemma. Such a singular case may occur in a situation where a given problem is overdetermined in the sense that it has more equations than unknowns. In this paper, based on these results, we propose a block-based adaptive multichannel super-exponential deflation algorithm. We present simulation results for the performance of the block-based algorithm in order to show the usefulness of the matrix pseudo-inversion lemma.

Recently we develop two kinds of approaches, that is, the super-exponential method (SEM) and the eigenvector method (EVM), of which both can achieve the blind deconvolution for MIMO-IIR systems. It is shown that these methods are closely related each other. Based on this fact, we propose a new SEM incorporated with the EVM. Simulation results will be presented for showing the validity of the proposed method.

This paper presents eigenvector algorithms (EVAs) for blind deconvolution of multiple-input multiple-output infinite impulse response (MIMO-IIR) channels (convolutive mixtures). One of the attractive features of the proposed EVA is that it is insensitive to Gaussian noises which are added to the outputs of the channels; hence the proposed EVA is referred to as a "robust" eigenvector algorithm (REVA). Simulation results show the validity of the REVA.

This paper presents eigenvector algorithms (EVAs) for blind deconvolution (BD) of multiple-input multiple-output infinite impulse response (MIMO-IIR) channels (convolutive mixtures). Using the idea of reference signals, the EVA is derived. Differently from the conventional researches on EVAs, one of the novel points of the paper is that the EVA using any reference signal is applied to the BD problem of the MIMO-IIR system, and then the validity of the EVA is shown.

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 + BBH)-1= A-1- A-1B(I + BHA-1B)-1BHA-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.

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.

This paper presents an eigenvector algorithm (EVA) derived from a criterion using reference signals, in which the EVA is applied to the blind source separation (BSS) of instantaneous mixtures. The proposed EVA works such that source signals are simultaneously separated from their mixtures. This is a new result, which has not been clarified by the conventional researches. Simulation results show the validity of the proposed EVA

The so called "super-exponential" methods (SEMs) are attractive methods for solving multichannel blind deconvolution problem. The conventional SEMs, however, have such a drawback that they are very sensitive to Gaussian noise. To overcome this drawback, the robust super-exponential method (RSEM) were proposed for single-input single-output infinite impulse response (SISO-IIR) channels and for multi-input multi-output (MIMO) static channels (instantaneous mixtures). While the conventional SEMs use the second- and higher-order cumulants of observations, the RSEM uses only the higher-order cumulants of observations. Since higher-order cumulants are insensitive to Gaussian noise, the RSEM is robust to Gaussian noise. We proposed an RSEM extended to the case of MIMO-IIR channels (convolutive mixtures). To show the validity of the proposed RSEM, some simulation results are presented

Separation of EEG (Electroencephalography) or MEG (Magnetoencephalography) data into activations of small dipoles or current density distribution is an ill-posed problem in which the number of parameters to estimate is larger than the dimension of the data. Several constraints have been proposed and used to avoid this problem, such as minimization of the L1-norm of the current distribution or minimization of Laplacian of the distribution. In this paper, we propose another biologically plausible constraint, sparseness of spatial difference of the current distribution. By numerical experiments, we show that the proposed method estimates current distribution well from both data generated by strongly localized current distributions and data generated by currents broadly distributed.

This paper presents an eigenvector algorithm (EVA) derived from a criterion using reference signals, in which the EVA is applied to the blind source separation (BSS) of instantaneous mixtures. The proposed EVA works such that source signals are simultaneously separated from their mixtures. This is a new result, which has not been clarified by the conventional researches. Moreover, by modifying the criterion, the corresponding EVA which is robust to Gaussian noise is derived. Simulation results show the validity of the proposed EVAs

The so called "super-exponential" methods (SEMs) are attractive methods for solving multichannel blind deconvolution problem. The conventional SEMs, however, have such a drawback that they are very sensitive to Gaussian noise. To overcome this drawback, the robust super-exponential method (RSEM) was proposed for single-input single-output infinite impulse response (SISO-IIR) channels and for multi-input multi-output (MIMO) static channels (instantaneous mixtures). While the conventional SEMs use the second- and higher-order cumulants of observations, the RSEM uses only the higher-order cumulants of observations. Since higher-order cumulants are insensitive to Gaussian noise, the RSEM is robust to Gaussian noise. We proposed an RSEM extended to the case of MIMO-IIR channels (convolutive mixtures). To show the validity of the proposed RSEM, some simulation results are presented

Separation of EEG (electroencephalography) or MEG (magnetoencephalography) data into activations of small dipoles or current density distribution is an ill-posed problem in which the number of parameters to estimate is larger than the dimension of the data. Several constraints have been proposed and used to avoid this problem, such as minimization of the L1-norm of the current distribution or minimization of Laplacian of the distribution. In this paper, we propose another constraint that the current density distribution changes at only a small number of areas and these changes can be large. By numerical experiments, we show that the proposed method estimates current distribution well from both data generated by strongly localized current distributions and data generated by currents broadly distributed

Blind source separation (BSS) tries to decompose a given multivariate data set into the product of a mixing matrix and a source vector, both of which are unknown. The sources can be recovered if we pose additional constraints to this model. One class of BSS algorithms is given by algebraic BSS, which recovers the mixing structure by jointly diagonalizing various source condition matrices corresponding to different source models. We review classical BSS algorithms such as FOBI, JADE, AMUSE, SOBI, TDSEP and SONS within this framework; combination of the respective source conditions can then yield additional algorithms as implemented e.g. by JADETD. Extensions to dependent component analysis models such as spatiotemporal or multidimensional BSS are discussed

The present paper deals with a signal separation technique, which can be applied, to the ears of robots. When we want a robot to recognize a desired signal in a situation where there are some noises (undesired signals), there exists such a case that the robot cannot recognize the desired signal. In this case, one must consider of separating the desired signal from the mixtures of it and the undesired signals. In the present paper, we propose a method in which such a separation problem can be solved. Experimental results show that our proposed method can solve successfully the signal separation problem.

The letter proposes a new iterative deflation algorithm to solve the blind source-factor separation for the outputs of multiple-input-multiple-output finite-impulse response (MIMO-FIR) channels driven by source signals that are temporally correlated but spatially uncorrelated. Using the proposed algorithm, filtered versions of the source signals, each of which is the contribution of each source signal to the outputs of MIMO-FIR channels, are extracted one by one from the mixtures of source signals.

In this paper, we propose a new iterative algorithm to solve the blind deconvolution problem of MIMO-FIR channels driven by source signals which are temporally second-order uncorrelated but fourth-order correlated and spatially second- and fourth-order uncorrelated. In our new approach, to solve the blind deconvolution problem, we consider two stages: First, filtered source signals are extracted from the mixtures of source signals. Second, the source signals are recovered from the filtered source signals.

The goal of the article is to find a minimal amount of statistical information (or a much weaker condition) about source signals for which blind equalization is possible for multiple-input multiple-output finite-impulse response (MIMO-FIR) channels. First, a sufficiently broad framework is set up within which such a theoretical problem is well posed. Within this framework, it is shown that second-order statistics (SOS) alone are not sufficient for blind equalization when the source signals are white. Additional higher order statistics (HOS) are needed. Then we show that the only additional higher order statistical information needed is spatial fourth-order cumulants. Though it has not yet been proved to be minimal, it is interesting to note that this is the same as the weakest known condition on the source signals even for an instantaneous mixture. We then show a necessary and sufficient condition for blind equalization when the source signals are white and spatially fourth-order uncorrelated. Based on this condition, criterion (A) for blind equalization of MIMO-FIR channels is developed by exploiting the temporal fourth-order statistics. Finally, based on this criterion, a new necessary and sufficient condition in terms of cumulants for the blind equalization of MIMO-FIR channels is obtained.

We consider the blind deconvolution problem of FIR multiple-input multiple-output channel systems. The systems-theoretic foundation is established on the broadest class of equalizable channel systems. This class of equalizable channel systems is then characterized. Based on this characterization, a fundamental factorization property, called irreducible-allpass factorization, is shown. Based on this fact, it is shown that any equalizable FIR system can and only can be converted to a paraunitary system, through the whitening of the observations, using the second-order statistics. The current second order statistics techniques considered only those channel systems that are irreducible, only half of the irreducible-allpass factorization of equalizable channels.

This paper addresses the blind deconvolution of multi-input-multi-output (MIMO) FIR systems driven by white non-Gaussian source signals. First, we present a weaker condition on source signals than the so-called i.i.d. condition so that blind deconvolution is possible. Then, under this condition, we provide a necessary and sufficient condition for blind deconvolution of MIMO FIR systems. Finally, based on this result, we propose two maximization criteria for blind deconvolution of MIMO FIR systems. These criteria are simple enough to be implemented by adaptive algorithms.

Multichannel blind deconvolution has received increasing attention during the last decade. Martone (see Proc. ICC '95, p.1505-08, 1995) extended the super-exponential method proposed by Shalvi and Weinstein (see IEEE Trans. Inform. Theory, vol.39, p.504-19, 1993, and Blind Deconvolution New Jersey: Prentice-Hall, p.121-80, 1994) for single-channel blind deconvolution to multichannel blind deconvolution. However, the Martone extension suffers from two types of serious drawbacks. The objective of this paper is to obviate these drawbacks and to propose three approaches to multichannel blind deconvolution. In the first approach, we present a multichannel super-exponential algorithm. In the second approach, we present a super-exponential deflation algorithm. In the third approach, we present a two-stage super-exponential algorithm.

In order to attain multichannel blind deconvolution of linear time-invariant nonminimum-phase dynamic systems. Inouye and Habe (see Proc. IEEE Signal Processing Workshop on Higher-Order Statistics, p.96-100, 1995) proposed 1995 a single-stage maximization criterion. The criterion function is the sum of squared fourth-order cumulants of the equalizer outputs, and the coefficients of the equalizer are determined at once. On the other hand, one of possible approaches for multichannel blind deconvolution is to construct an equalizer based on the system identified by higher-order cumulant-matching. In this paper, it is shown that the single-stage maximization criterion is equivalent to a least-squares fourth-order cumulant-matching criterion after multichannel pre-whitening of channel outputs. This result provides us with an important interpretation of the single-stage maximization criterion.

This paper deals with the problem of identification of multichannel linear systems driven by unobservable colored inputs based on higher-order statistics of the outputs. Let S be the set of scalar stable transfer functions. We define the notion of a generalized permutation matrix (g-matrix) over S and that of a shift matrix (s-matrix). It is shown that the transfer function matrix of an unknown system is identified up to post-multiplication of the product of a g-matrix and a s-matrix. This result is applied to identifying FIR systems for blind signal separation.>

An identifiability result for the blind identification of memoryless channels with independent sources is presented. The necessary and sufficient conditions which were obtained by investigating the eigenstructure inherited in the observation cumulants are given. An eigenstructure-based algorithm is proposed to achieve the identification of the parameter matrix whenever such identification is possible. It is shown that the source signals can be extracted up to scale factors and a permutation if and only if all the source signals, but one, are non-Gaussian.>

An iterative algorithm for the identification of multichannel moving average (MA) processes driven by mutually independent and identically distributed (i.i.d.) input signals is proposed. It is shown that the algorithm has a finite-step global convergence property. This algorithm is computationally efficient and numerically stable. Two multichannel MA models, including one nonminimum-phase MA model, are estimated by this algorithm with satisfactory performances. It is shown that this algorithm guarantees a solution of third-order cumulant-based identification equations.>

Given finite samples of a stationary, perhaps noisy, nonGaussian r-variate moving-average, MA(q) process, the authors study cumulant based identifiability conditions, under which the MA coefficient matrices, the input statistics, and the order q, can be uniquely determined. The selection of a unique representative from the equivalence class corresponding to a given cumulant structure involves less restrictions than that corresponding to a given covariance structure. They derive two algorithms for estimating the (possibly) nonminimum phase MA coefficient matrices.>