Explicit signal to noise ratio in reproducing kernel Hilbert spaces

This paper introduces a nonlinear feature extraction method based on kernels for remote sensing data analysis. The proposed approach is based on the minimum noise fraction (MNF) transform, which maximizes the signal variance while also minimizing the estimated noise variance. We here propose an alternative kernel MNF (KMNF) in which the noise is explicitly estimated in the reproducing kernel Hilbert space. This enables KMNF dealing with non-linear relations between the noise and the signal features jointly. Results show that the proposed KMNF provides the most noise-free features when confronted with PCA, MNF, KPCA, and the previous version of KMNF. Extracted features with the explicit KMNF also improve hyperspectral image classification.