PCA and LDA in DCT domain

In this paper, we prove that the principal component analysis (PCA) and the linear discriminant analysis (LDA) can be directly implemented in the discrete cosine transform (DCT) domain and the results are exactly the same as the one obtained from the spatial domain. In some applications, compressed images are desirable to reduce the storage requirement. For images compressed using the DCT, e.g., in JPEG or MPEG standard, the PCA and LDA can be directly implemented in the DCT domain such that the inverse DCT transform can be skipped and the dimensionality of the original data can be initially reduced to cut down computational cost.