I'm actually studying how to perform a PCA-based image compression. In Hernandez & Mendez's Application of Principal Component Analysis to Image Compression, an approach to compute the Principal Component Analysis for image compression is proposed. This approach involve the division of the original image in a set of non-overlapping patches with a fixed dimension (i.e., 8x8): the various patches are rearranged in some row vectors in order to build the data matrix on which PCA is performed. I don't understand what is the theoretical justification for which the image is divided into different patches. What is the difference between considering directly the matrix which representes the image and then, compute the associated covariance matrix? And, last but not least, what is the effect of the patch-size on the overall process?