Logarithmic Kernel Relaxed Collaborative Representation With Scaled MST Dictionary Construction for Hyperspectral Anomaly Detection

Representation-based anomaly detection methods are one of the most popular methods in hyperspectral anomaly detection. Nevertheless, linear models of have difficulties in adequately describing complex data and generating a decision boundary for anomaly-background separation. To relax such a limitation, a novel kernel relaxed collaboration representation anomaly detection method is proposed. A new logarithmic kernel function is used to map the raw data into a high-dimensional feature space where anomalies and background are more separable. Meanwhile, the scaled minimum spanning tree method is adopted to cluster the data and select representative pixels to construct a pure dictionary. Then, the distance from a testing pixel to each dictionary atom is calculated using the KNN method, and atoms with the closest distance are selected to construct a nonglobal dictionary for the testing pixel. The proposed method becomes more robust due to the contamination of anomalies from the dictionary is removed. The experiments on four real datasets demonstrate that the proposed method has significant advantages over currently existing methods.