Temporal and Spectral Processing Methods for Processing of Degraded Speech: A Review <s> BSS and ICA Methods <s> Higher-order multivariate statistics are addressed. A theoretical discussion is followed by an original application. A special (index-free) tensor formalism to express fourth-order multivariate statistics is proposed. A quadricovariance tensor which contains the fourth-order joint cumulants is defined. In this formalism, the quadricovariance tensor and its eigen-matrices are natural fourth-order generalizations of second-order covariance and eigenvectors, allowing direct extension of many standard second-order method to fourth-order. The idea of an eigen-matrix is then proposed as a solution to the blind source separation problem. The task is to separate a mixture of N independent non-Gaussian signals received on an array of sensors when no information is available about propagation conditions or array geometry (blind situation). This can be achieved only by resorting to higher-order information. Quadricovariance eigen-matrices give a direct solution to this problem. > <s> BIB001 </s> Temporal and Spectral Processing Methods for Processing of Degraded Speech: A Review <s> BSS and ICA Methods <s> Abstract The separation of independent sources from an array of sensors is a classical but difficult problem in signal processing. Based on some biological observations, an adaptive algorithm is proposed to separate simultaneously all the unknown independent sources. The adaptive rule, which constitutes an independence test using non-linear functions, is the main original point of this blind identification procedure. Moreover, a new concept, that of INdependent Components Analysis (INCA), more powerful than the classical Principal Components Analysis (in decision tasks) emerges from this work. <s> BIB002 </s> Temporal and Spectral Processing Methods for Processing of Degraded Speech: A Review <s> BSS and ICA Methods <s> Abstract The independent component analysis (ICA) of a random vector consists of searching for a linear transformation that minimizes the statistical dependence between its components. In order to define suitable search criteria, the expansion of mutual information is utilized as a function of cumulants of increasing orders. An efficient algorithm is proposed, which allows the computation of the ICA of a data matrix within a polynomial time. The concept of ICA may actually be seen as an extension of the principal component analysis (PCA), which can only impose independence up to the second order and, consequently, defines directions that are orthogonal. Potential applications of ICA include data analysis and compression, Bayesian detection, localization of sources, and blind identification and deconvolution. <s> BIB003 </s> Temporal and Spectral Processing Methods for Processing of Degraded Speech: A Review <s> BSS and ICA Methods <s> Blind signal separation (BSS) and independent component analysis (ICA) are emerging techniques of array processing and data analysis that aim to recover unobserved signals or "sources" from observed mixtures (typically, the output of an array of sensors), exploiting only the assumption of mutual independence between the signals. The weakness of the assumptions makes it a powerful approach, but it requires us to venture beyond familiar second order statistics, The objectives of this paper are to review some of the approaches that have been developed to address this problem, to illustrate how they stem from basic principles, and to show how they relate to each other. <s> BIB004 </s> Temporal and Spectral Processing Methods for Processing of Degraded Speech: A Review <s> BSS and ICA Methods <s> Two array signal processing techniques are combined with independent component analysis (ICA) to enhance the performance of blind separation of acoustic signals in a reflective environment. The first technique is the subspace method which reduces the effect of room reflection when the system is used in a room. Room reflection is one of the biggest problems in blind source separation (BSS) in acoustic environments. The second technique is a method of solving permutation. For employing the subspace method, ICA must be used in the frequency domain, and precise permutation is necessary for all frequencies. In this method, a physical property of the mixing matrix, i.e., the coherency in adjacent frequencies, is utilized to solve the permutation. The experiments in a meeting room showed that the subspace method improved the rate of automatic speech recognition from 50% to 68% and that the method of solving permutation achieves performance that closely approaches that of the correct permutation, differing by only 4% in recognition rate. <s> BIB005 </s> Temporal and Spectral Processing Methods for Processing of Degraded Speech: A Review <s> BSS and ICA Methods <s> In this paper, a prototype of novel algorithm for blind separation of convolutive mixtures of audio sources is proposed. The method works in time-domain, and it is based on the recently very successful algorithm EFICA for Independent Component Analysis, which is an enhanced version of more famous FastICA. Performance of the new algorithm is very promising, at least, comparable to other (mostly frequency domain) algorithms. Audio separation examples are included. <s> BIB006 </s> Temporal and Spectral Processing Methods for Processing of Degraded Speech: A Review <s> BSS and ICA Methods <s> The paper presents comparative assessment of Blind Source Separation methods for instantaneous mixtures. The study highlights the underlying principles of Principal Component Analysis (PCA) and Independent Component Analysis (ICA) in this context. These methods have been tested on instantaneous mixtures of synthetic periodic signals, monotonous noise from electromechanical systems and speech signals. In particular, methods based on Nonlinear PCA, Maximum Entropy, Mutual Information Minimization and Fast ICA, have been compared for their separation ability, processing time and accuracy. The quality of the output, the complexity of the algorithms and the simplicity (implementation) of the methods are some of the performance measures which are highlighted with respect to the above signals. <s> BIB007
Recently, blind source separation (BSS) by independent component analysis (ICA) has received great attention. Blind separation of instantaneous mixture is achieved by the ICA, which aims at decomposing the multivariate data into a linear sum of independent components BIB003 . The goal in BSS is to recover a set of independent sources, given only a set of sensor observations that are generated from the individual source signals, through an unknown linear mixing process BIB004 . In BSS research, there are two important problems that are generally considered: Instantaneous BSS and convolutive BSS. In the case of instantaneous BSS, signals are mixed instantaneously. However, in a practical environment, signals are always mixed in a convolutive manner, because of the reverberation effects. The BSS technique in speech signal separation was first attempted by Cardoso BIB001 and Jutten BIB002 , using the principle of statistical independence of the sources BIB004 . Blind separation of multiple speakers was attempted where the coefficients of the finite impulse response (FIR) filters were used to represent the linear mixing of the sources. These algorithms were based on the higher order statistics of the signal's mutual independence measure among the independent components. Later, numerous approaches have been presented using ICA in BSS for speech separation BIB005 BIB006 BIB007 . Even though a variety of algorithms have been proposed, all ICA algorithms are fundamentally similar. The main difference between the different ICA algorithms is the numerical algorithm used for measuring the signal independence. The basic ICA approach uses the following linear model  : where the vector S represents m independent sources, the matrix A represents the linear mixing of the sources, and the vector X is composed of m observed signals. The idea of the ICA is to recover the original sources by assuming that they are statistically independent. The independence assumption means that the joint PDF is the product of the densities for all sources.