A least squares algorithm for global joint decomposition of complex matrix sets

This paper deals with a new approach for the joint decomposition of complex matrix sets. Such problems arise naturally in various signal processing problems, among which the blind source separation one. The suggested algorithm is based on an Alternating Least Square (ALS) optimization procedure. An improved version is also proposed including a global Enhanced Line Search (ELS) in the recursive procedure. In practice, the main interest of our approach is to take advantage of a greater amount of signal information within the same context, since sets of Hermitian and symmetric complex matrices are combined altogether. Simulations are performed to highlight the advantages of this method as compared to other existing algorithms.

[1]  El Mostafa Fadaili,et al.  Nonorthogonal Joint Diagonalization/Zero Diagonalization for Source Separation Based on Time-Frequency Distributions , 2007, IEEE Transactions on Signal Processing.

[2]  Eric Moreau,et al.  A generalization of joint-diagonalization criteria for source separation , 2001, IEEE Trans. Signal Process..

[3]  Tülay Adali,et al.  A relative gradient algorithm for joint decompositions of complex matrices , 2010, 2010 18th European Signal Processing Conference.

[4]  Driss Aboutajdine,et al.  Gradient-based joint block diagonalization algorithms: Application to blind separation of FIR convolutive mixtures , 2010, Signal Process..

[5]  Pierre Comon,et al.  Enhanced Line Search: A Novel Method to Accelerate PARAFAC , 2008, SIAM J. Matrix Anal. Appl..

[6]  Bernard C. Picinbono,et al.  On circularity , 1994, IEEE Trans. Signal Process..

[7]  Arie Yeredor,et al.  Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separation , 2002, IEEE Trans. Signal Process..

[8]  J. Cardoso,et al.  Blind beamforming for non-gaussian signals , 1993 .

[9]  Arie Yeredor,et al.  Approximate Joint Diagonalization Using a Natural Gradient Approach , 2004, ICA.

[10]  Hicham Ghennioui,et al.  A Nonunitary Joint Block Diagonalization Algorithm for Blind Separation of Convolutive Mixtures of Sources , 2007, IEEE Signal Processing Letters.

[11]  Xianda Zhang,et al.  An improved signal-selective direction finding algorithm using second-order cyclic statistics , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[12]  Bart De Moor,et al.  On the blind separation of non-circular sources , 2002, 2002 11th European Signal Processing Conference.

[13]  Rasmus Bro,et al.  MULTI-WAY ANALYSIS IN THE FOOD INDUSTRY Models, Algorithms & Applications , 1998 .

[14]  Andrzej Cichocki,et al.  Regularized Alternating Least Squares Algorithms for Non-negative Matrix/Tensor Factorization , 2007, ISNN.

[15]  Joe Brewer,et al.  Kronecker products and matrix calculus in system theory , 1978 .