Non-orthogonal joint block diagonalization based on the LU or QR factorizations for convolutive blind source separation

This article addresses the problem of blind source separation, in which the source signals are most often of the convolutive mixtures, and moreover, the source signals cannot satisfy independent identical distribution generally. One kind of prevailing and representative approaches for overcoming these difficulties is joint block diagonalization (JBD) method. To improve present JBD methods, we present a class of simple Jacobi-type JBD algorithms based on the LU or QR factorizations. Using Jacobi-type matrices we can replace high dimensional minimization problems with a sequence of simple one-dimensional problems. The novel methods are more general i.e. the orthogonal, positive definite or symmetric matrices and a preliminary whitening stage is no more compulsorily required, and further, the convergence is also guaranteed. The performance of the proposed algorithms, compared with the existing state-of-the-art JBD algorithms, is evaluated with computer simulations and vibration experimental. The results of numerical examples demonstrate that the robustness and effectiveness of the two novel algorithms provide a significant improvement i.e., yield less convergence time, higher precision of convergence, better success rate of block diagonalization. And the proposed algorithms are effective in separating the vibration signals of convolutive mixtures

Convolutive Blind Source Separation Methods

In this chapter, we provide an overview of existing algorithms for blind source separation of convolutive audio mixtures. We provide a taxonomy, wherein many of the existing algorithms can be organized, and we present published results from those algorithms that have been applied to real-world audio separation tasks

Blind Separation of Independent Sources from Convolutive Mixtures

International audienceThe 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 para-unitary 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

Penalty function-based joint diagonalization approach for convolutive blind separation of nonstationary sources

A new approach for convolutive blind source separation (BSS) by explicitly exploiting the second-order nonstationarity of signals and operating in the frequency domain is proposed. The algorithm accommodates a penalty function within the cross-power spectrum-based cost function and thereby converts the separation problem into a joint diagonalization problem with unconstrained optimization. This leads to a new member of the family of joint diagonalization criteria and a modification of the search direction of the gradient-based descent algorithm. Using this approach, not only can the degenerate solution induced by a unmixing matrix and the effect of large errors within the elements of covariance matrices at low-frequency bins be automatically removed, but in addition, a unifying view to joint diagonalization with unitary or nonunitary constraint is provided. Numerical experiments are presented to verify the performance of the new method, which show that a suitable penalty function may lead the algorithm to a faster convergence and a better performance for the separation of convolved speech signals, in particular, in terms of shape preservation and amplitude ambiguity reduction, as compared with the conventional second-order based algorithms for convolutive mixtures that exploit signal nonstationarity

Joint Tensor Factorization and Outlying Slab Suppression with Applications

We consider factoring low-rank tensors in the presence of outlying slabs. This problem is important in practice, because data collected in many real-world applications, such as speech, fluorescence, and some social network data, fit this paradigm. Prior work tackles this problem by iteratively selecting a fixed number of slabs and fitting, a procedure which may not converge. We formulate this problem from a group-sparsity promoting point of view, and propose an alternating optimization framework to handle the corresponding $\ell_p$ ($0<p\leq 1$) minimization-based low-rank tensor factorization problem. The proposed algorithm features a similar per-iteration complexity as the plain trilinear alternating least squares (TALS) algorithm. Convergence of the proposed algorithm is also easy to analyze under the framework of alternating optimization and its variants. In addition, regularization and constraints can be easily incorporated to make use of \emph{a priori} information on the latent loading factors. Simulations and real data experiments on blind speech separation, fluorescence data analysis, and social network mining are used to showcase the effectiveness of the proposed algorithm

Blind Signal Separation for Digital Communication Data

to appear in EURASIP E-reference in Signal Processing, invited paper.International audienceBlind source separation, often called independent component analysis , is a main field of research in signal processing since the eightees. It consists in retrieving the components, up to certain indeterminacies, of a mixture involving statistically independent signals. Solid theoretical results are known; besides, they have given rise to performent algorithms. There are numerous applications of blind source separation. In this contribution, we particularize the separation of telecommunication sources. In this context, the sources stem from telecommunication devices transmitting at the same time in a given band of frequencies. The received data is a mixed version of all these sources. The aim of the receiver is to isolate (separate) the different contributions prior to estimating the unknown parameters associated with a transmitter. The context of telecommunication signals has the particularity that the sources are not stationary but cyclo-stationary. Now, in general, the standard methods of blind source separation assume the stationarity of the sources. In this contribution , we hence make a survey of the well-known methods and show how the results extend to cyclo-stationary sources

Blind separation of convolutive mixtures based on second order and third order statistics

This paper addresses the problem of blind separation of linear convolutive mixtures. We first reformulate the problem into a blind separation of linear instantaneous mixtures, and then a statistical approach is applied to solve the reformulated problem. From the statistics of the mixtures, two kinds of matrix pencils are constructed to estimate the mixing matrix. The original sources are then separated with the estimated mixing matrix. For the purpose of computational efficiency and robustness, in the matrix pencil, one matrix is constructed from the second order statistics, and the other is constructed from the third order statistics. The proposed novel methods do not require the exact knowledge of the channel order. Simulation results show that the methods are robust and have good performance.published_or_final_versio