Paper Info
Title
Semi-nonnegative joint diagonalization by congruence and semi-nonnegative ICA.
Abstract
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-ALSexp and CGexp, 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.
Year
DOI
Venue
2014
10.1016/j.sigpro.2014.05.017
Signal Processing
Keywords
Field
DocType
Semi-nonnegative joint diagonalization by congruence,Semi-nonnegative ICA,Optimization methods,Matrix calculation,Magnetic resonance spectroscopy,Image analysis
Change of variables,Mathematical optimization,Matrix calculus,Matrix (mathematics),A priori and a posteriori,Image processing,Line search,Independent component analysis,Congruence (geometry),Mathematics
Journal
Volume
ISSN
Citations 
105
0165-1684
3
PageRank 
References 
Authors
0.44
19
5
Name
Order
Citations
PageRank
Julie Coloigner141.50
Laurent Albera225024.44
Amar Kachenoura39312.88
Fanny Noury430.44
Lotfi Senhadji524231.96