An Alternating Direction Method of Multipliers for Constrained Joint Diagonalization by Congruence (Invited Paper)

Lu Wang (1, 2, 3) , Laurent Albera (4, 1, 3) , Lotfi Senhadji (1, 3) , Jean-Christophe Pesquet (5)

1 LTSI - Laboratoire Traitement du Signal et de l'Image
2 Information Technology Head Office, Guotai Junan Securities Co., Ltd.
3 CRIBS - Centre de Recherche en Information Biomédicale sino-français
4 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
5 LIGM - Laboratoire d'Informatique Gaspard-Monge

In this paper, we address the problem of joint diagonalization by congruence (i.e. the canonical polyadic decomposition of semi-symmetric 3rd order tensors) subject to arbitrary convex constraints. Sufficient conditions for the existence of a solution are given. An efficient algorithm based on the Alternating Direction Method of Multipliers (ADMM) is then designed. ADMM provides an elegant approach for handling the additional constraint terms, while taking advantage of the structure of the objective function. Numerical tests on simulated matrices show the benefits of the proposed method for low signal to noise ratios. Simulations in the context of nuclear magnetic resonance spectroscopy are also provided.

Domaines: Ingénierie biomédicale; Traitement du signal et de l'image [eess.SP]

Lu Wang, Laurent Albera, Lotfi Senhadji, Jean-Christophe Pesquet. An Alternating Direction Method of Multipliers for Constrained Joint Diagonalization by Congruence (Invited Paper). 2015 IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Dec 2015, Cancun, Mexico. pp.197-200, ⟨10.1109/CAMSAP.2015.7383770⟩. ⟨hal-01245119⟩