On non-unique 2-D filter bank shapes and their lifting-based designs

For a given two-dimensional down-sampling, the alias-free ideal filter bank shapes are not unique. In this work finding such shapes and designing such filter banks is investigated. A schematic way to obtain such ideal filter shapes is suggested. Several examples are considered to show how to obtain interesting ideal filter shapes. While known two-dimensional filter bank design schemes cater to specific shapes, a universal design procedure based on lifting is used in this work to design these filter banks.