Interference rejection approach to noise adjusted principal components transform

A signal-to-noise ratio based PCA approach, called Maximum Noise Fraction (MNF) transformation or Noise Adjusted Principal Components (NAPC) transform PCA was recently developed to arrange principal components in decreasing order of image quality rather than data variance as done for PCA. One of major disadvantages of this approach is that the noise covariance matrix must be estimated accurately from the data a priori. Another is that the factor of interference is not taken into account in MNF or NAPC where the effect of interference tends to be more serious than noise in hyperspectral images. In this paper, these two problems are addressed by considering the interference as a separate unwanted signal source from which an interference rejection approach to noise adjusted principal components transform (IRNAPC) can be developed in a similar manner that the NAPC was derived. It is shown that if interference is taken care of properly, IRNAPC significantly improves NAPC. Additionally, interference annihilation also improves the estimation of the noise covariance matrix.