Randomized RX for Target Detection

Abstract

This work tackles the target detection problem through the well-known global RX method. The RX method models the clutter as a multivariate Gaussian distribution, and has been extended to nonlinear distributions using kernel methods. While the kernel RX can cope with complex clutters, it requires a considerable amount of computational resources as the number of clutter pixels gets larger. Here we propose random Fourier features to approximate the Gaussian kernel in kernel RX and consequently our development keep the accuracy of the nonlinearity while reducing the computational cost which is now controlled by an hyperparameter. Results over both synthetic and real-world image target detection problems show space and time efficiency of the proposed method while providing high detection performance.

Efficient Nonlinear RX Anomaly Detectors

“…We propose using feature map and low-rank approximation approaches to improve the efficiency of the KRX detector. We study the following approximations to the KRX method: Random Fourier features (RRX) previously studied by the authors in [6], orthogonal random features (ORX), naive low-rank approximation (LRX), and Nyström low-rank approximation (NRX).…”

“…and leads to a nonlinear randomized RX (RRX) [6] that approximates the KRX. Essentially, we map the original data x i into a nonlinear space through the explicit mapping z(x i ) to a 2D-dimensional space (instead of the potentially infinite feature space with φ(x i )), and then use the linear RX formula.…”

“…In order to undertake this challenge, we propose to use efficient techniques based on random Fourier features and low-rank approximations to obtain improved performance of the KRX algorithm. We reported our initial efforts using the random Fourier features approach in [6] In the literature, local and global RX-based detectors have been proposed. In local AD [2], pixels in a sliding window are used as input data.…”