A Convex Analysis Framework for Blind Separation of Non-Negative Sources

• Published in: IEEE transactions on signal processing Vol. 56; no. 10; pp. 5120 - 5134
• Main Authors: CHAN, Tsung-Han, MA, Wing-Kin, CHI, Chong-Yung, YUE WANG
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.10.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Acoustic signal processing; Acoustical engineering; Applied sciences; Biomedical imaging; Biomedical signal processing; Blind separation; Blind source separation; Blinds; Convex analysis; convex analysis criterion; convex optimization; Councils; Criteria; Detection, estimation, filtering, equalization, prediction; Dominance; Effectiveness; Exact sciences and technology; Geometry; Independent component analysis; Information, signal and communications theory; linear program; Linear programming; Miscellaneous; non-negative sources; Separation; Signal and communications theory; Signal processing; Signal, noise; simplex geometry; Simulation; Source separation; Speech processing; Studies; Telecommunications and information theory; Convex analysis criterion; Convex optimization; Simplex geometry; Non-negative sources; Linear program; Blind separation; Linear programming; linear program; Blind source separation; Convex programming; non-negative sources; Simulation; convex analysis criterion; Signal processing; convex optimization; simplex geometry; Deterministic approach; Multiple channel; Convex analysis; Biomedical imaging
• DOI: 10.1109/TSP.2008.928937
• ISSN: 1053-587X

This paper presents a new framework for blind source separation (BSS) of non-negative source signals. The proposed framework, referred herein to as convex analysis of mixtures of non-negative sources (CAMNS), is deterministic requiring no source independence assumption, the entrenched premise in many existing (usually statistical) BSS frameworks. The development is based on a special assumption called local dominance. It is a good assumption for source signals exhibiting sparsity or high contrast, and thus is considered realistic to many real-world problems such as multichannel biomedical imaging. Under local dominance and several standard assumptions, we apply convex analysis to establish a new BSS criterion, which states that the source signals can be perfectly identified (in a blind fashion) by finding the extreme points of an observation-constructed polyhedral set. Methods for fulfilling the CAMNS criterion are also derived, using either linear programming or simplex geometry. Simulation results on several data sets are presented to demonstrate the efficacy of the proposed method over several other reported BSS methods.