Nonnegative Joint Diagonalization by Congruence Based on LU Matrix Factorization

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.

Keywords

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

Domains

Bioengineering Signal and Image processing Signal and Image Processing Optimization and Control [math.OC]

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https://inserm.hal.science/inserm-00841128

Submitted on : Sunday, July 7, 2013-5:31:49 PM

Last modification on : Thursday, April 18, 2024-4:27:45 PM

Long-term archiving on: Wednesday, April 5, 2017-7:00:45 AM

Dates and versions

inserm-00841128 , version 1 (07-07-2013)

Identifiers

HAL Id : inserm-00841128 , version 1
DOI : 10.1109/LSP.2013.2267797

Cite

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⟩

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