On the design of two-channel 2-D nonseparable multi-plet perfect reconstruction filter banks

This paper proposes a new design method for a class of two-channel 2D non-separable perfect reconstruction (PR) filter banks (FBs) using the multi-plet FBs. 1D multi-plet FBs are PR FBs that can be obtained by frequency transformation of a prototype PR FB in the conventional lifting structure so that a better frequency characteristics can be obtained and varied online to process different signals. By employing the ID to 2D transformation of Phoong et al, new 2D PR multi-plet FBs with quincunx, hourglass, and parallelogram spectral support are obtained. These nonseparable multi-plet FBs can be cascaded to realize new PR directional FB for image processing and motion analysis. The design procedure is very general and it can be applied to both linear-phase and low-delay 2D FBs. Design examples are given to demonstrate the usefulness of the proposed method.