Blind separation of non-negative sources by convex analysis: Effective method using linear programming

Abstract

We recently reported a criterion for blind separation of non-negative sources, using a new concept called convex analysis for mixtures of non-negative sources (CAMNS). Under some assumptions that are considered realistic for sparse or high-contrast signals, the criterion is that the true source signals can be perfectly recovered by finding the extreme points of some observation-constructed convex set. In our last work we also developed methods for fulfilling the CAMNS criterion, but only for two to three sources. In this paper we propose a systematic linear programming (LP) based method that is applicable to any number of sources. The proposed method has two advantages. First, its dependence on LP means that the method does not suffer from local minima. Second, the maturity of LP solvers enables efficient implementation of the proposed method in practice. Simulation results are provided to demonstrate the efficacy of the proposed method.