Digital Affine Shear Filter Banks with 2-Layer Structure and Their Applications in Image Processing

Digital affine shear filter banks with 2-layer structure (DAS-2 filter banks) are constructed and are shown to be with the perfect reconstruction property. The implementation of digital affine shear transforms using the transition and subdivision operators are given. The redundancy rate analysis shows that our digital affine shear transforms have redundancy rate no more than 8 and it decreases with respect to the number of directional filters. Numerical experiments on image processing demonstrate the advantages of our DAS-2 filter banks over many other state-of-the-art frame-based transforms. The connection between DAS-2 filter banks and affine shear tight frames with 2-layer structure is established. Characterizations and constructions of affine shear tight frames with 2-layer structure are provided.