A Point-Set Topology-Based Information Entropy Estimation Method for Hyperspectral Target Detection

With hyperspectral remote sensors (imaging spectrometers) imaging a scene, the specificity of the target of interest is manifested in the significant differences between it and the surrounding background in terms of quantity, spatial distribution, and spectral characteristics, which provides conditions for the implementation of pixel-level diagnostics for target detection. Traditional model-driven methods utilize specific model assumptions to parse hyperspectral image (HSI) data in scenes with variability and are prone to encounter limitations due to model-data discrepancy. Most data-driven methods are limited in practical applications due to the great demand for training samples, the large number of parameters to be determined, and the costly computational complexity. To address the limitations of the existing methods, this article adopts point-set topology theories to analyze the properties of hyperspectral data at the mathematical-statistical level and seek a solution for the information retrieval task of target detection, whereby a target detection method through information entropy estimation based on point-set topology is proposed. First, parallel topological spaces are constructed to order the original HSI data to ensure that the differences in data features between various classes of land covers are reflected in intuitive properties in the topological spaces. Second, in conjunction with the priori information about the target, information entropy estimation is introduced to select optimal separable spaces for the target and the background by measuring the degree of ordering of data to achieve an accurate separation. Finally, a proper way to quantify and highlight the differences in data features between various land covers in the optimal separable spaces is explored for the algorithmic output to perform the information retrieval task. The proposed target detection through information entropy estimation based on point-set topology (TD-IEEPST) exploits an innovative combination of point set topology theories and information entropy estimation to achieve efficient extraction of land cover information for detection, ensuring both theoretical interpretability and computational efficiency. Extensive experimental results on real hyperspectral datasets verify that the proposed method is ahead of other widely used and state-of-the-art methods in terms of computational cost, detection effects, and robustness, and promising to provide technical support for detection response requirements in practical applications.