کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
563708 1451962 2014 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Semi-nonnegative joint diagonalization by congruence and semi-nonnegative ICA
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر پردازش سیگنال
پیش نمایش صفحه اول مقاله
Semi-nonnegative joint diagonalization by congruence and semi-nonnegative ICA
چکیده انگلیسی


• We focus on the semi-nonnegative joint diagonalization by congruence decomposition.
• This problem appears in semi-nonnegative independent component analysis.
• The nonnegative constraint is circumvented by means of exponential parametrization.
• We propose two novel algorithms, belonging to the line search strategy.
• Our algorithms are illustrated through semi-nonnegative ICA applications.

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Signal Processing - Volume 105, December 2014, Pages 185–197
نویسندگان
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