Constrained Nonnegative Matrix Factorization Based on Particle Swarm Optimization for Hyperspectral Unmixing

Spectral unmixing is an important part of hyperspectral image processing. In recent years, constrained nonnegative matrix factorization (CNMF) has been successfully applied for unmixing without the pure-pixel assumption and the result is physically meaningful. However, traditional CNMF algorithms always have two limitations: 1) Most of them are based on gradient methods and usually get trapped in a local optimum. 2) As they adopt static penalty function as the constraint handling method, it's difficult to choose a proper regularization parameter that can balance the tradeoff between reconstruction error and constraint well, which leads to the decreased accuracy. In this paper, we introduce particle swarm optimization (PSO) combined with two types of progressive constraint handling approaches for spectral unmixing in the framework of CNMF. A basic method called high-dimensional double-swarm PSO (HDPSO) algorithm is first proposed. It divides the original high-dimension problem into a series of easier subproblems and adopts two interactive swarms to search endmembers and abundances, respectively. Then, adaptive PSO (APSO) and multiobjective PSO algorithms are proposed by respectively incorporating adaptive penalty function and multiobjective optimization approaches into HDPSO. Experiments with both simulated data and real hyperspectral images are used to compare these methods with traditional algorithms and results validate that the proposed methods give better performance for spectral unmixing.