Information Entropy Estimation Based on Point-Set Topology for Hyperspectral Anomaly Detection

Xiaotong Sun, Lina Zhuang, Lianru Gao, Hongmin Gao, Xu Sun, Yi Liu, Yao Liu, Bing Zhang

Abstract: Anomaly detection is one of the most popular research topics in hyperspectral remote sensing. A variety of traditional model-driven methods fail to reveal features of data with diversity due to monotonous, fixed analytical modes. This paper analyzes mathematical-statistical properties of hyperspectral images (HSIs) and proposes an interesting approach of information entropy estimation based on point-set topology (IEEPST) to resolve anomaly detection from a brand new perspective, thus eliminating the limitations caused by the data-model discrepancy. Specifically, the original HSI data are mapped into topological spaces to enable ordered arrangements, in preparation for revealing data features. Particularly, information entropy estimation is introduced for the first time in the adoption of point-set topology to adequately unravel the data arrangements in topological spaces, whereby the land cover information is efficiently extracted for detection. Experimental results demonstrate that IEEPST accommodates both detection accuracy and computational efficiency, and is highly competitive with other sophisticated and state-of-the-art methods.