Similarity Constrained Convex Nonnegative Matrix Factorization for Hyperspectral Anomaly Detection

Abstract

Hyperspectral anomaly detection is very important in the remote sensing domain. The representation-based anomaly method is one of the most important hyperspectral anomaly detection methods, which uses reconstruction errors (REs) to detect anomalies. REs are affected by the basis matrix and its corresponding coefficient matrix. Mixed pixels exist because of the low-spatial resolution of hyperspectral images. The RE is not large enough to correctly distinguish the pixel difficult to classify when the basis matrix is composed of pixels. Moreover, its corresponding coefficients cannot indicate whether pixels are pure or mixed and the abundances of mixed pixels. To address the above-mentioned problems, endmembers referring to pure or relatively pure spectral signatures are explored to build the basis matrix. The RE based on the basis matrix of endmembers is much larger for the anomalous pixel difficult to correctly classify. Furthermore, its corresponding coefficient matrix of endmembers has physical meanings. Hence, a novel hyperspectral anomaly detection based on similarity constrained convex nonnegative matrix factorization is proposed from the perspective of endmembers for the first time. First, convex nonnegative matrix factorization (CNMF) is employed to obtain endmembers of background. Then, CNMF is constrained by the similarity regularization that considers different contributions of endmembers to the pixel under test to acquire the more accurate and meaningful coefficient matrix. Finally, anomalies are detected by calculating REs. The proposed algorithm is verified on both simulated and real data sets. Experimental results show that our proposed algorithm outperforms other state-of-the-art algorithms.