Multidimensional PRCC filter banks and matched sampling systems

We derive general expressions for filters in multidimensional interpolation and approximation sampling systems matched to the input process. We then estimate the mean square error between the reconstructed and the original processes for these systems. We next describe the extension of the perfect reconstruction circular convolution filter bank (PRCC) framework to two-dimensions for the specific case of filter banks based on qunicunx sampling. We conclude by discussing how the matched sampling systems can be used in the PRCC framework in potential applications such as image coding.