A theory of recursive kernel RX anomaly detection algorithm for hyperspectral imagery

With the development of imaging spectroscopy and the improvement of spectral resolution, the ever-expending hyperspectral datasets lead to huge pressure of data storage, downlink transmission and further processing. Real-time processing which requires immediate decision making is greatly desired in hyperspectral anomaly detection. Kernel Reed-Xiaoli detector (KRXD) is a kernel-based nonlinear version of RXD, it achieves better detection accuracy but inferior detection efficiency. This paper developments a new modified KRXD based on progressive line processing that can implement real-time detection in a line-by-line fashion. A new local causal framework is defined to remain the causality of detection system. Aiming at the defect that the complexities of KRXD is high in calculating the detection process, taking advantage of the Woodbury matrix identity and the matrix inversion lemma to recursively update the kernel Gram matrix and its inversion to meet the requirement of rapid processing. Experimental results show the proposed method significantly solves real-time processing problem and keep detection accuracy unchanged compared to the initial algorithm.