Structured dictionary learning with 2-D non-separable oversampled lapped transform

This work proposes a novel design method of a two-dimensional (2-D) Non-Separable Oversampled Lapped Transform (NSOLT) for a given image by introducing a typical two stage procedure of dictionary learning. NSOLT is a lattice-structure-based transform and yields a redundant dictionary of which atoms satisfy the non-separable, symmetric, real-valued, overlapping and compact-support property. In addition, the Parseval tight frame constraint can structurally be imposed, while the redundancy R is flexibly controlled by the ratio of the number of channels P and the downsampling ratio M. Compared with the other dictionary learning approaches, the proposed method is moderately structured so that it is capable of multiscale construction as well as atom termination at image boundary. The significance of the proposed method is verified by showing an example of learned dictionary and sparse approximation results.