2-D two-channel lifting based filter bank design to allow switching between filter banks

Switching between 2-D filter banks is important in constructing 2-D adaptive transforms, and lifting factorization has been at the heart of many successful 2-D adaptive transforms. However, switching between filter banks with arbitrary number of lifting steps will induce transients in the transition region between the filter banks. In this paper, we derive conditions on lifting steps of a 2-D two-channel filter bank such that switching between filter banks designed with such conditions will not induce transients. We design 2-D directional filter banks with the proposed conditions, and show successful switching between them within an adaptive directional transform for image coding.