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ispartof: Signal Processing vol:198 status: published

Although CPA (canonical/parallel factor analysis) has a unique solution, the actual computation can be made more robust by incorporating extra constraints. In several applications, the factors in one mode are known to be statistically independent. On the other hand, in Independent Component Analysis (ICA), it often makes sense to impose a Khatri-Rao structure on the mixing vectors. In this paper, we propose a new algorithm to impose independence constraints in CPA. Our algorithm implements the algebraic CPA structure and the property of statistical independence simultaneously. Numerical experiments show that our method outperforms in several cases pure CPA, pure ICA, and tensor ICA, a previously proposed method for combining ICA and CPA. We also present a strategy for imposing full or partial symmetry in CPA.

Independent Component Analysis (ICA) aims at blindly decomposing a linear mixture of independent sources. It has lots of applications in diverse research areas. In some applications, there is prior knowledge on the sources and/or the mixing vectors. This prior knowledge can be incorporated in the computation of the independent sources. In this paper we provide an algorithm for so-called spatially constrained ICA (scICA). The algorithm deals with the situation when one mixing vector is exactly known. Also the generalization to more mixing vectors is discussed. Numerical experiments are reported that allow us to assess the improvement in accuracy that can be achieved with these algorithms compared to fully blind ICA and to a previously proposed constrained algorithm. We illustrate the approach with a biomedical application.

In this paper, we introduce an enhanced line search algorithm to accelerate the convergence of the alternating least squares (ALS) algorithm, which is often used to decompose a tensor in a sum of contributions. This scheme can be used for the computation in the complex case of the Parallel Factor model or the more general block component model. We then illustrate the performance of the algorithm in the context of blind separation-equalization of convolutive DS-CDMA mixtures.

In this paper we present new deterministic tensor-based techniques for the blind separation of a mixture of DS-CDMA signals received by an antenna array. First, we show that the blind receiver follows from a simultaneous matrix decomposition. We present a new, relaxed, bound on the number of users that can be allowed at the same time. We further derive two algorithms that jointly exploit the CDMA structure and the constant modulus property of the transmitted signals.

In this paper we develop a technique for detecting and retrieving the common harmonics in a multi-channel setup. The different (complex) signals are arranged in a set of Hankel matrices. First, we compute the singular value decomposition (SVD) of these matrices in order to denoise and normalize the relevant subspaces. Then a second SVD is applied to detect and select the common subspace. The poles of the harmonics are computed from the common subspace using the total least squares (TLS) technique. This method is very flexible, robust and outperforms existing subspace-based methods. Moreover, it can be applied to an arbitrary number of channels.