Some invariance properties of the minimum noise fraction transform

The Minimum Noise Fraction (MNF) transform is widely used in the remote sensing and image processing communities, because it is usually better than the Principal Components (PC) transform at compressing and ordering multispectral and hyperspectral images in terms of image “quality”. The MNF transform is also invariant to invertible (i.e. non-singular) linear transformations of multispectral/hyperspectral data, a property not shared by the PC transform. This general invariance property of the MNF transform is proved. Three examples of the general invariance property are provided and discussed: (i) invariance to scaling, (ii) invariance to certain types of background correction, and (iii) invariance to different types of noise.