Semi-nonnegative joint diagonalization by congruence and semi-nonnegative ICA

被引:5
|
作者
Coloigner, Julie [1 ,2 ]
Albera, Laurent [1 ,2 ,3 ]
Kachenoura, Amar [1 ,2 ]
Noury, Fanny [1 ,2 ]
Senhadji, Lotfi [1 ,2 ]
机构
[1] INSERM, UMR 1099, F-35000 Rennes, France
[2] Univ Rennes 1, LTSI, F-35000 Rennes, France
[3] INRIA Rennes Bretagne Atlantique, F-35000 Rennes, France
关键词
Semi-nonnegative joint diagonalization by congruence; Semi-nonnegative ICA; Optimization methods; Matrix calculation; Magnetic resonance spectroscopy; Image analysis; INDEPENDENT COMPONENT ANALYSIS; BLIND SOURCE SEPARATION; LEAST-SQUARES; TENSOR DECOMPOSITIONS; ALGORITHMS; SEARCH; MODEL;
D O I
10.1016/j.sigpro.2014.05.017
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
In this paper, we focus on the Joint Diagonalization by Congruence (JDC) decomposition of a set of matrices, while imposing nonnegative constraints on the joint diagonalizer. The latter will be referred to the semi-nonnegative JDC fitting problem. This problem appears in semi-nonnegative Independent Component Analysis (ICA), say ICA involving nonnegative static mixtures, such as those encountered for instance in image processing and in magnetic resonance spectroscopy. In order to achieve the semi-nonnegative JDC decomposition, we propose two novel algorithms called ELS-ALS(exp) and CG(exp), which optimize an unconstrained problem obtained by means of an exponential change of variable. The proposed methods are based on the line search strategy for which an analytic global plane search procedure has been considered. All derivatives have been jointly calculated in matrix form using the algebraic basis for matrix calculus and product operator properties. Our algorithms have been tested on synthetic arrays and the semi-nonnegative ICA problem is illustrated through simulations in magnetic resonance spectroscopy and in image processing. The numerical results show the benefit of using a priori information, such as nonnegativity. (c) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码:185 / 197
页数:13
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