Jacobi-like nonnegative joint diagonalization by congruence

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

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

A new joint diagonalization by congruence algorithm is presented, which allows the computation of a nonnegative joint diagonalizer. The nonnegativity constraint is ensured by means of a square change of variable. Then we propose a Jacobi-like approach using LU matrix factorization, which consists of formulating a high-dimensional optimization problem into several sequential one-dimensional subproblems. Numerical experiments emphasize the advantages of the proposed method, especially in the presence of bottlenecks such as for low SNR values and a small number of available matrices. An illustration of blind source separation shows the interest of the proposed algorithm.

Mots clés: Nonnegative joint diagonalization by congruence; LU factorization; blind source separation; seminonnegative independent component analysis.; seminonnegative independent component analysis

Domaines: Analyse numérique [math.NA]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Lu Wang, Laurent Albera, Huazhong Shu, Lotfi Senhadji. Jacobi-like nonnegative joint diagonalization by congruence. XXI European Signal Processing Conference (EUSIPCO'13), Sep 2013, Marrakech, Morocco. 5 p. ⟨hal-00921807⟩