Nonnegative Joint Diagonalization by Congruence Based on LU Matrix Factorization

Lu Wang (1, 2) , Laurent Albera (3, 1) , Amar Kachenoura (1) , Huazhong Shu (2, 4) , Lotfi Senhadji (1)

1 LTSI - Laboratoire Traitement du Signal et de l'Image
2 CRIBS - Centre de Recherche en Information Biomédicale sino-français
3 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
4 LIST - Laboratory of Image Science and Technology [Nanjing]

In this letter, a new algorithm for joint diagonalization of a set of matrices by congruence is proposed to compute the nonnegative joint diagonalizer. The nonnegativity constraint is imposed by means of a square change of variables. Then we formulate the high-dimensional optimization problem into several sequential polynomial subproblems using LU matrix factorization. Numerical experiments on simulated matrices emphasize the advantages of the proposed method, especially in the case of degeneracies such as for low SNR values and a small number of matrices. An illustration of blind separation of nuclear magnetic resonance spectroscopy confirms the validity and improvement of the proposed method.

Mots clés: Blind source separation; independent component analysis; LU factorization; nonnegative joint diagonalization by congruence; nuclear magnetic resonance spectroscopy

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

Lu Wang, Laurent Albera, Amar Kachenoura, Huazhong Shu, Lotfi Senhadji. Nonnegative Joint Diagonalization by Congruence Based on LU Matrix Factorization. IEEE Signal Processing Letters, 2013, 20 (8), pp.807 - 810. ⟨10.1109/LSP.2013.2267797⟩. ⟨inserm-00841128⟩