Interference and noise-adjusted principal components analysis

The goal of principal components analysis (PCA) is to find principal compon ents in accordance with maximum variance of a data matrix, However, it has been shown recently that such variance-based principal components may not a dequately represent image quality. As a result, a modified PCA approach bas ed on maximization of SNR was proposed, Called maximum noise fraction (MNF) transformation or noise-adjusted principal components (NAPC) transform, it arranges principal components in decreasing order of image quality rather than variance. One of the 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 M NF or NAPC in which the interfering effect tends to be more serious than no ise in hyperspectral images, In this paper, these two problems are addresse d by considering the interference as a separate, unknown signal source, fro m which an interference and noise-adjusted principal components analysis (I NAPCA) can be developed in a manner similar to the one from which the NAPC was derived. Two approaches are proposed for the INAPCA, referred to as sig nal to interference plus noise ratio-based principal components analysis (S INR-PCA) and interference-annihilated noise-whitened principal components a nalysis (IANW-PCA), It is shown that if interference is taken care of prope rly, SINR-PCA and IANW-PCA significantly improve NAPC. In addition, interfe rence annihilation also improves the estimation of the noise covariance mat rix. All of these results are compared with NAPC and PCA and are demonstrat ed by HYDICE data.