Fast Real-Time Kernel RX Algorithm Based on Cholesky Decomposition

Abstract

Real-time processing has attracted wide attention in hyperspectral anomaly detection. The traditional local real-time kernel RX detector (LRT-KRXD) is still with some computational limitations, which lower the processing speed and even damage the detection due to the matrix singularity. In this letter, we present LRT-KRXD based on Cholesky decomposition (LRT-KRXD-CD). First, the derivation of kernel covariance matrices is computationally expensive in KRXD, while each two adjacent matrices contain almost identical content. To remove the repeated computation, a recursive strategy for these kernel covariance matrices is used. Second, the kernel covariance matrix is symmetric positive definite after adding a diagonal matrix with small scale. With this property, Cholesky decomposition and linear system solving can be utilized to address the problem of inverse matrix. In this case, the detection of LRT-KRXD-CD becomes robust and its processing speed is improved as well. Experimental results on two hyperspectral images substantiate the effectiveness of LRT-KRXD-CD.