Minimum Noise Fraction versus Principal Component Analysis as a Preprocessing Step for Hyperspectral Imagery Denoising

Minimum noise fraction (MNF) is a well-known technique for hyperspectral imagery denoising. It transforms a noisy data cube into output channel images with steadily increasing noise levels, which means that the MNF output images contain steadily decreasing image quality. Principal component analysis (PCA) can also be used for hyperspectral imagery denoising. The PCA is defined in such a way that the first principal component has the largest possible variance, and each succeeding component has the highest variance possible under the constraint that it is orthogonal to the preceding components. It can be shown that these components are the Eigenvectors of the covariance matrix of the samples. In this study, we compare PCA-based methods with MNF-based methods for hyperspectral imagery denoising. Our comparison consists of the following 3 steps: (1) forward MNF/PCA transform of a noisy hyperspectral data cube; (2) reduce noise in selected output channel images with index k > k(0), a channel number cutoff threshold; (3) inverse MNF/PCA transform of the noise-reduced channel images to obtain the denoised hyperspectral data cube. Our experiments demonstrate that MNF-based methods achieve higher signal-to-noise ratios than PCA-based methods for signal-dependent noise, whereas PCA-based methods produce higher SNRs than MNF-based methods for Gaussian white noise.