Sampling systems matched to the input image class

The authors present closed form expressions for filters in interpolation and approximation sampling systems, given the sampling lattice and matched to the input image class in the mean squared sense. We also derive expressions for the mean squared error incurred in both the systems while reconstructing individual images of the input class from their samples. For the approximation sampling case, we show that the optimal filters are spectral factors of a brickwall-type filter whose support is determined by the sampling lattice. Finally, we present examples of filters in interpolation and approximation sampling cases that are matched to an image class derived from a multispectral image. The performance of these filters is tested in the presence of a quantizer for different bit rates and is compared with that of some standard filters.