Yujiro Inouye

Waveform-preserving blind estimation of multiple independent sources

The problem of blind estimation of source signals is to estimate the source signals without knowing the characteristics of the transmission channel. It is shown that the minimum-variance unbiased estimates can be obtained if and only if the transmission channel can be identified blindly. It is shown that the channel can be blindly identified if and only if there is not more than one Gaussian source. This condition suggests that waveform-preserving blind estimation can be achieved over a wide range of signal processing applications, including those cases in which the source signals have identical nonGaussian distributions. The constructive proof of the necessary and sufficient condition serves as a foundation for the development of waveform-preserving blind signal estimation algorithms. Examples are presented to demonstrate the applications of the theoretical results. >

Cumulant based identification of multichannel moving-average models

Given cumulants of a stationary, perhaps noisy, non-Gaussian r-variate moving average, MA(q) process, identifiability conditions are studied, 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 fewer restrictions than that corresponding to a given covariance structure. Two algorithms are derived for estimating the (possibly) nonminimum-phase MA coefficient matrices. >

A system-theoretic foundation for blind equalization of an FIR MIMO channel system

The system-theoretic foundation for blind equalization of a finite-impulse response (FIR) MIMO channel system in the channel-filter setting is investigated. In this setting, a general definition of equalizable channel system is presented, and its characterization is given: Every equalizable channel system has an FIR irreducible-paraunitary factorization. Based on this fact, we show that any equalizable channel system can be reduced to a paraunitary FIR system by a filter, called a whitener. It is shown that one such whitener can be designed by a linear prediction-based approach. It is also shown that if the original FIR channel system has no transmission zero at the origin, then the above paraunitary FIR channel system is a static system.

Cumulant-based blind identification of linear multi-input-multi-output systems driven by colored inputs

The blind identification problem of a linear multi-input-multi-output (MIMO) system is widely noticed by many researchers in diverse fields due to its relevance to blind signal separation. However, such a problem is ill-posed and has no unique solution. Therefore, we can only find a solution of the problem within an equivalence class. We address the blind identification problem of the linear MIMO system driven by unobservable colored inputs using higher order statistics (HOS), particularly the fourth-order cumulants, of the outputs, where the unobservable inputs are mutually independent but temporally colored linear processes. We first define the set, which is denoted by S, of stable scalar transfer functions and then define the notion of a generalized permutation matrix (which is abbreviated by a g-matrix) over S. Then, it is shown that the transfer function matrix of an unknown system is identified only up to post-multiplication by a g matrix. This result is applied to identifying FIR systems for blind signal separation.

Super-exponential algorithms for multichannel blind deconvolution

Multichannel blind deconvolution has been receiving increasing attention. Shalvi and Weinstein proposed an attractive approach to single-channel blind deconvolution called the super-exponential methods. The objective of this correspondence is to extend the Shalvi and Weinstein (1993, 1994) approach to the multichannel case and present super-exponential algorithms for multichannel blind deconvolution. We propose three approaches to multichannel blind deconvolution. In the first one, we present a multichannel super-exponential algorithm. In the second one, we present a super-exponential deflation algorithm. In the third one, we present a two-stage super-exponential algorithm.

A finite-step global convergence algorithm for the parameter estimation of multichannel MA processes

An iterative algorithm for the identification of multichannel moving average (MA) processes using higher-order statistics is proposed. It is shown that the algorithm has a finite-step global convergence property. Three multichannel MA models, including one nonminimum-phase MA model, are estimated by this algorithm with satisfactory performances. >

Paper: Approximation of multivariable linear systems with impulse response and autocorrelation sequences

This paper considers the construction of approximants of multi-input-multi-output, discrete-time linear systems from the finite data of the impulse response and autocorrelation sequences. In the approximation of a multivariable linear system, it is common practice to use a finite portion of its impulse response sequence. This is formally equivalent to the Pade approximation technique, which may produce unstable approximants, even though the original system is stable. Mullis and Roberts proposed a new method, which yields stable approximants, in connection with approximation of digital filters. This is, however, restricted to the single-input-single-output case. This paper extends their method to the multi-input-multi-output case and shows a fast recursive algorithm to construct stable approximants of linear systems.

Iterative algorithms based on multistage criteria for multichannel blind deconvolution

Blind deconvolution and blind equalization have been important interesting topics in diverse fields including data communication, image processing, and geophysical data processing. Recently, Inouye and Habe introduced a multistage criterion for attaining blind deconvolution of multiple-input multiple-output (MIMO) linear time-invariant (LTI) systems. In this correspondence, based on their criterion, we present iterative algorithms for solving the blind deconvolution problem of MIMO LTI systems. However, their criterion should be subjected to several constraints of equations. Therefore, they proposed a new constraint-free multistage criterion for accomplishing the blind deconvolution of MIMO LTI systems. Based on their unconstrained criterion, we show iterative algorithms for solving the blind deconvolution of multichannel LTI systems.

Criteria for blind deconvolution of multichannel linear time-invariant systems

Blind deconvolution and equalization of linear time-invariant systems have widely received attention in various fields such as data communication, image processing and geophysical data processing. Shalvi and Weinstein (1990) proposed certain criteria for blind deconvolution of nonminimum-phase linear time-invariant systems. Their work is, however, restricted to the single-channel (or scalar) case. This correspondence extends the Shalvi-Weinstein approach to the multichannel case. We propose a multistage maximization criterion and a single-stage maximization criterion for attaining multichannel blind deconvolution. Under the normalized condition specified later, they are shown to be equivalent.

On the use of joint diagonalization in blind signal processing

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