Principal Components transform with simple, automatic noise adjustment

A new form of the Principal Components transform is described which is particularly suited for use with hyperspectral image data, such as the images produced by the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). This new transform scales or adjusts the image data in each band by an estimate of the noise in each band. The noise estimates are simply made from the image data itself through the inverse of its covariance matrix. For reasons associated with this, the transform is called a 'Residual-scaled' PC or RPC transform. The inversion of the covariance matrix is the only extra computation required over and above that needed for the ordinary PC transform. The RPC transform corresponds to using a diagonal noise matrix with the Maximum Noise Fraction transform or the Noise-Adjusted PC transform. Its performance is compared with that of the ordinary PC and the Standardized PC transforms for 102 bands of a 1992 AVIRIS image of a vegetated area (the Jasper Ridge Biological Preserve). Its low-order, high-variance components are of consistently better quality than theirs. The Standardized PC transform performs poorly with such hyperspectral data and should be used with caution, if at all.