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.

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