Two dimensional nonuniform perfect reconstruction filter bank with irrational down-sampling matrices

In this paper, we propose a new method to realize an irrational scaling of a 2D digital signal/image. This method is suitable for any scaling matrices with real entries, including irrational numbers. Based on this algorithm, a new structure of a 2D four-channel non-uniform perfect reconstruction filter bank is derived. Through the proposed structure, it is now possible to segment the 2D frequency components of a 2D digital signal/image arbitrarily through a careful design of the scaling matrix while still preserving the PR property. Therefore, we can find many applications such as image compression and communication using this structure. The experimental results are presented at the end of this paper.