Relative gradient based algorithms for general joint diagonalization of complex matrices

This article deals with the problem of joint diagonalization of hermitian and/or complex symmetric matrices. Within the framework of gradient algorithms, we develop various algorithms which are based on different levels of approximation of the classical diagonalization criterion. The algorithms are based on a multiplicative update and on the derivation of an optimal step-size. One of the algorithms is a generalization of DOMUNG to the complex case. Finally, in the blind source separation context, computer simulations illustrate the relative performances of some proposed algorithms in comparison to the true gradient one.

[1]  R. E. Hudson,et al.  DOA estimation method for wideband color signals based on least-squares Joint Approximate Diagonalization , 2008, 2008 5th IEEE Sensor Array and Multichannel Signal Processing Workshop.

[2]  Eric Moreau,et al.  High order contrasts for self-adaptive source separation criteria for complex source separation , 1996 .

[3]  Pierre Comon,et al.  Gradient based Approximate Joint Diagonalization by orthogonal transforms , 2008, 2008 16th European Signal Processing Conference.

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

[5]  Visa Koivunen,et al.  Complex random vectors and ICA models: identifiability, uniqueness, and separability , 2005, IEEE Transactions on Information Theory.

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

[7]  X. Q. Yang,et al.  A New Gradient Method with an Optimal Stepsize Property , 2006, Comput. Optim. Appl..

[8]  M. Wax,et al.  A least-squares approach to joint diagonalization , 1997, IEEE Signal Processing Letters.

[9]  Eric Moreau,et al.  Joint Matrices Decompositions and Blind Source Separation , 2014 .

[10]  Heinz Mathis,et al.  Joint diagonalization of correlation matrices by using gradient methods with application to blind signal separation , 2002, Sensor Array and Multichannel Signal Processing Workshop Proceedings, 2002.

[11]  Eric Moreau,et al.  Variations around gradient like algorithms for joint diagonalization of hermitian matrices , 2012, 2012 Proceedings of the 20th European Signal Processing Conference (EUSIPCO).

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

[13]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[14]  J. Idier,et al.  Convergence of Conjugate Gradient Methods with a Closed-Form Stepsize Formula , 2008 .

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

[16]  Eric Moreau,et al.  Blind Identification and Separation of Complex-Valued Signals: Moreau/Blind Identification and Separation of Complex-Valued Signals , 2013 .

[17]  Anthony J. Weiss,et al.  Array processing using joint diagonalization , 1996, Signal Process..

[18]  Arie Yeredor,et al.  Joint Matrices Decompositions and Blind Source Separation: A survey of methods, identification, and applications , 2014, IEEE Signal Processing Magazine.

[19]  Christian Jutten,et al.  Detection de grandeurs primitives dans un message composite par une architecture de calcul neuromime , 1985 .

[20]  Pierre Comon,et al.  Handbook of Blind Source Separation: Independent Component Analysis and Applications , 2010 .