Optimal filters for multidimensional sampling and reconstruction of image classes

This paper deals with multidimensional sampling and optimal reconstruction of the input random field or image class in the mean squared sense. It considers the interpolation and approximation sampling systems and presents closed form expressions for the filters in these systems as well as the mean squared errors between the input and the reconstructed fields. For the approximation sampling systems the optimal filters turn out to be spectral factors of an ideal brickwall filter whose support is determined by the sampling lattice. Finally, it presents examples of filters matched to an input image class derived from a multispectral LANDSAT image. In an image coding context, these filters can be considered as providing the best tradeoff between coding rate reduction by undersampling and distortion in reconstruction. 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 to demonstrate this