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

As one of the most active research hotspots in hyperspectral remote sensing, anomaly detection is widely used because it takes effect without any priori information about the target or the background. Most of the traditional model-driven methods fail to reveal features of data with diversity due to fixed analytical modes. A variety of data-driven methods encounter difficulties in practical applications due to their costly computational complexity. In this article, an innovative combination of point-set topology and information entropy theories is utilized to analyze the mathematical-statistical properties of hyperspectral images (HSIs), thus eliminating the limitations caused by the data-model discrepancy. Specifically, the original HSI data are mapped into topological spaces in a specific form to enable ordered arrangements, in preparation for revealing data features. In particular, 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. Accordingly, an interesting approach of information entropy estimation based on point-set topology (IEEPST) is proposed to resolve anomaly detection from a brand new perspective, pursuing prominent detection accuracy while ensuring computational efficiency. The experimental results on benchmark HSI datasets demonstrate that IEEPST achieves detection performance with high probabilities of detection (PD) and low false alarm rates (FARs) at an inexpensive computational cost. The proposed IEEPST is highly competitive with other sophisticated and state-of-the-art methods.