Traditionally

the most commonly used sampling lattice in image processing systems is the rectangular sampling lattice. However

when the signal is a circularly band-limited

the minimum sampling density for a hexagonal sampling lattice is 13.4% less than that for a rectangular sampling lattice. This result is one of the most attractive reasons for considering the hexagonal sampling lattice as an alternative to the rectangular lattice. Almost all the input/output devices only support the rectangular sampled digital images

so the transformation between the hexagonal sampling lattice and the rectangular sampling lattice is discussed in this paper

and the hexagonal sampling matrix satisfied Nyquist Sampling Theorem is given. Moreover hexagonal sampled digital images are non-separable signals. It is difficult to process a non-separable signal directly. In this paper

a multiresolution decomposition of hexagonal sampled images based on a separable filter bank is proposed. A multi-scale decomposition structure is obtained with low computation complexity

and the reconstructed image is presented.