The goal of principal components analysis (PCA) is to find principal components in accordance with maximum variance of a data matrix. However, it has been shown recently that such variance-based principal components may not adequately represent image quality. As a result, a modified PCA approach based 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 MNF or NAPC in which the interfering effect 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, unknown signal source, from which an interference and noise-adjusted principal components analysis (INAPCA) 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 signal to interference plus noise ratio-based principal components analysis (SINR-PCA) and interference-annihilated noise-whitened principal components analysis (IANW-PCA). It is shown that if interference is taken care of properly, SINR-PCA and IANW-PCA significantly improve NAPC. In addition, interference annihilation also improves the estimation of the noise covariance matrix. All of these results are compared with NAPC and PCA and are demonstrated by HYDICE data.