The transformation of a data set using a second-order polynomial mapping to find statistically independent components is considered (quadratic independent component analysis or ICA). Based on overdetermined linear ICA, an algorithm together with separability conditions are given via linearization reduction. The linearization is achieved using a higher dimensional embedding defined by the linear parametrization of the monomials, which can also be applied for higher-order polynomials. The paper finishes with simulations for artificial data and natural images.

We newly propose a novel blind separation framework for Single-Input Multiple-Output (SIMO)-model-based acoustic signals using an extended ICA algorithm, SIMO-ICA. The SIMO-ICA consists of multiple ICAs and a fidelity controller, and each ICA runs in parallel under the fidelity control of the entire separation system. The SIMO-ICA can separate the mixed signals, not into monaural source signals but into SIMO-model-based signals from independent sources as they are at the microphones. Thus, the separated signals of SIMO-ICA can maintain the spatial qualities of each sound source. In order to evaluate its effectiveness, separation experiments are carried out under both nonreverberant and reverberant conditions. The experimental results reveal that the signal separation performance of the proposed SIMO-ICA is the same as that of the conventional ICA-based method, and that the spatial quality of the separated sound in SIMO-ICA is remarkably superior to that of the conventional method, particularly for the fidelity of the sound reproduction.

This paper describes a real-time blind source separation (BSS) method for moving speech signals in a room. Our method employs frequency domain independent component analysis (ICA) using a blockwise batch algorithm in the first stage, and the separated signals are refined by postprocessing using crosstalk component estimation and non-stationary spectral subtraction in the second stage. The blockwise batch algorithm achieves better performance than an online algorithm when sources are fixed, and the postprocessing compensates for performance degradation caused by source movement. Experimental results using speech signals recorded in a real room show that the proposed method realizes robust real-time separation for moving sources. Our method is implemented on a standard PC and works in realtime.

We propose a new algorithm for overdetermined blind source separation (BSS) based on multistage independent component analysis (MSICA). To improve the separation performance, we have proposed MSICA in which frequency-domain ICA and time-domain ICA are cascaded. In the original MSICA, the specific mixing model, where the number of microphones is equal to that of sources, was assumed. However, additional microphones are required to achieve an improved separation performance under reverberant environments. This leads to alternative problems, e.g., a complication of the permutation problem. In order to solve them, we propose a new extended MSICA using subarray processing, where the number of microphones and that of sources are set to be the same in every subarray. The experimental results obtained under the real environment reveal that the separation performance of the proposed MSICA is improved as the number of microphones is increased.

In this paper a new adaptive multi-input multi-output (MIMO) channel estimation and multiuser detection algorithm based kernel space iterative inversion is proposed. The functions of output signals are mapped from a low dimensional space to a high dimensional reproducing kernel Hilbert space. The function of the output signals is represented as a linear combination of a set of basis functions, and a Mercer kernel function is constructed by the distribution function. In order to avoid finding the function f(.) and g(.), the correlation among the output signals is calculated in the low dimension space by the kernel. Moreover, considering the practical application, the algorithm is extended to online iteration of mixture system. The computer simulation results illustrated that the new algorithm increase the performance of channel estimation, the global convergence, and the system stability.

We newly propose a stable algorithm for blind source separation (BSS) combining multistage ICA (MSICA) and linear prediction. The MSICA is the method previously proposed by the authors, in which frequency-domain ICA (FDICA) for a rough separation is followed by time-domain ICA (TDICA) to remove residual crosstalk. For temporally correlated signals, we must use TDICA with a nonholonomic constraint to avoid the decorrelation effect from the holonomic constraint. However, the stability cannot be guaranteed in the nonholonomic case. To solve the problem, the linear predictors estimated from the roughly separated signals by FDICA are inserted before the holonomic TDICA as a prewhitening processing, and the dewhitening is performed after TDICA. The stability of the proposed algorithm can be guaranteed by the holonomic constraint, and the pre/dewhitening processing prevents the decorrelation. The experiments in a reverberant room reveal that the algorithm results in higher stability and separation performance.

An adaptive blind signal separation filter is proposed using a risk-sensitive criterion framework. This criterion adopts an exponential type function. Hence, the proposed criterion varies the consideration weight of an adaptation quantity depending on errors in the estimates: the adaptation is accelerated when the estimation error is large, and unnecessary acceleration of the adaptation does not occur close to convergence. In addition, since the algorithm derivation process relates to an H filtering, the derived algorithm has robustness to perturbations or estimation errors. Hence, this method converges faster than conventional least squares methods. Such effectiveness of the new algorithm is demonstrated by simulation.

We propose a new algorithm for blind source separation (BSS), in which frequency-domain independent component analysis (FDICA) and time-domain ICA (TDICA) are combined to achieve a superior source-separation performance under reverberant conditions. Generally speaking, conventional TDICA fails to separate source signals under heavily reverberant conditions because of the low convergence in the iterative learning of the inverse of the mixing system. On the other hand, the separation performance of conventional FDICA also degrades significantly because the independence assumption of narrow-band signals collapses when the number of subbands increases. In the proposed method, the separated signals of FDICA are regarded as the input signals for TDICA, and we can remove the residual crosstalk components of FDICA by using TDICA. The experimental results obtained under the reverberant condition reveal that the separation performance of the proposed method is superior to those of TDICA- and FDICA-based BSS methods.

We propose a new algorithm for blind source separation (BSS), in which independent component analysis (ICA) and beamforming are combined to resolve the low-convergence problem through optimization in ICA. The proposed method consists of the following two parts: frequency-domain ICA with direction-of-arrival (DOA) estimation, and null beamforming based on the estimated DOA. The alternation of learning between ICA and beamforming can realize fast- and high-convergence optimization. The results of the signal separation experiments reveal that the signal separation performance of the proposed algorithm is superior to that of the conventional ICA-based BSS method.

In many applications of Independent Component Analysis (ICA) and Blind Source Separation (BSS) estimated sources signals and the mixing or separating matrices have some special structure or some constraints are imposed for the matrices such as symmetries, orthogonality, non-negativity, sparseness and specified invariant norm of the separating matrix. In this paper we present several algorithms and overview some known transformations which allows us to preserve several important constraints.

In this paper we consider blind source separation (BSS) problem of signals which are spatially uncorrelated of order four, but temporally correlated of order four (for instance speech or biomedical signals). For such type of signals we propose a new sufficient condition for separation using fourth order statistics, stating that the separation is possible, if the source signals have distinct normalized cumulant functions (depending on time delay). Using this condition we show that the BSS problem can be converted to a symmetric eigenvalue problem of a generalized cumulant matrix Z(4)(b) depending on L-dimensional parameter b, if this matrix has distinct eigenvalues. We prove that the set of parameters b which produce Z(4)(b) with distinct eigenvalues form an open subset of RL, whose complement has a measure zero. We propose a new separating algorithm which uses Jacobi's method for joint diagonalization of cumulant matrices depending on time delay. We empasize the following two features of this algorithm: 1) The optimal number of matrices for joint diago- nalization is 100-150 (established experimentally), which for large dimensional problems is much smaller than those of JADE; 2) It works well even if the signals from the above class are, additionally, white (of order two) with zero kurtosis (as shown by an example).

A new blind identification method of transfer functions between variables in feedback systems is introduced for single sweep type of MEG data. The method is based on the viewpoint of stochastic/statistical inverse problems. The required conditions of the model are stationary and linear Gaussian processes. Raw MEG data of the brain activities are heavily contaminated with several noises and artifacts. The elimination of them is a crucial problem especially for the method. Usually, these noises and artifacts are removed by notch and high-pass filters which are preset automatically. In the present paper, we will try two types of more careful preprocessing procedures for the identification method to obtain impulse functions. One is a careful notch filtering and the other is a blind source separation method based on temporal structure. As results, identifiably of transfer functions and their impulse responses are improved in both cases. Transfer functions and impulse responses identified between MEG sensors are obtained by using the method in Appendix A, when eyes are closed with rest state. Some advantages of the blind source separation method are discussed.

The problem of separating blindly independent sources from a convolutive mixture cannot be addressed in its widest generality without resorting to statistics of order higher than two. The core of the problem is in fact to identify the paraunitary part of the mixture, which is addressed in this paper. With this goal, a family of statistical contrast is first defined. Then it is shown that the problem reduces to a Partial Approximate Joint Diagonalization (PAJOD) of several cumulant matrices. Then, a numerical algorithm is devised, which works block-wise, and sweeps all the output pairs. Computer simulations show the good behavior of the algorithm in terms of Symbol Error Rates, even on very short data blocks.

We propose a new intelligent blind source separation algorithm for the mixture of sub-Gaussian and super-Gaussian sources. The algorithm consists of an update equation of the separating matrix and an adjustment equation of nonlinear functions. To verify the validity of the proposed algorithm, we compare the proposed algorithm with extant methods.

We propose a blind source separation algorithm for the mixture of finite alphabet sources where sensors are less than sources. The algorithm consists of an update equation of an estimated mixing matrix and enumeration of the inferred sources. We present the bound of a step size for the stability of the algorithm and two methods of assignment of the initial point of the estimated mixing matrix. Simulation results verify the proposed algorithm.

In this paper, we discuss a neural network approach for blind signal extraction of temporally correlated sources. Assuming autoregressive models of source signals, we propose a very simple neural network model and an efficient on-line adaptive algorithm that extract, from linear mixtures, a temporally correlated source with an arbitrary distribution, including a colored Gaussian source and a source with extremely low value (or even zero) of kurtosis. We then combine these extraction processing units with deflation processing units to extract such sources sequentially in a cascade fashion. Theory and simulations show that the proposed neural network successfully extracts all arbitrarily distributed, but temporally correlated source signals from linear mixtures.

We present a cascade neural network for blind source extraction. We propose a family of unconstrained optimization criteria, from which we derive a learning rule that can extract a single source signal from a linear mixture of source signals. To prevent the newly extracted source signal from being extracted again in the next processing unit, we propose another unconstrained optimization criterion that uses knowledge of this signal. From this criterion, we then derive a learning rule that deflates from the mixture the newly extracted signal. By virtue of blind extraction and deflation processing, the presented cascade neural network can cope with a practical case where the number of mixed signals is equal to or larger than the number of sources, with the number of sources not known in advance. We prove analytically that the proposed criteria both for blind extraction and deflation processing have no spurious equilibria. In addition, the proposed criteria do not require whitening of mixed signals. We also demonstrate the validity and performance of the presented neural network by computer simulation experiments.

Electronic systems are progressively replacing mechanical devices or human operation for identifying people or objects in everyday-life applications. Especially, the contactless identification systems available today have several advantages, but they cannot handle easily several simultaneously present items. This paper describes a solution to this problem, based on blind source separation techniques. The effectiveness of this approach is experimentally demonstrated, especially by using a real-time DSP-based implementation of the proposed system.