Multidimensional matched sampling systems and PRCC filter banks

General expressions for filters in multidimensional interpolation and approximation sampling systems matched to the input random field are derived. Expressions for the mean squared error between the reconstructed and the original random fields are obtained. The perfect reconstruction circular convolution filter bank (PRCC) framework is extended 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.