Design of two-dimensional PR quincunx filter banks with Euler-Frobenius polynomial and lifting scheme

Two-dimensional (2-D) filter banks (FBs) have played a significant role in retrieving the directional information of images. In this paper, we propose a technique to design 2-D two-channel perfect reconstruction (PR) FBs with quincunx sampling. The proposed design method comprises two stages. In the first stage, we propose the design of a new halfband polynomial using Euler-Frobenius polynomial (EFP). This is constructed by imposing vanishing moment and PR constraints on EFP. The resulting new polynomial is a maximally flat Euler-Frobenius halfband polynomial (EFHBP). Later, in the second stage, EFHBP is used in a modified 2-D lifting scheme to design 2-D filters. The design examples for 2-D filters are presented and compared to existing filters. The performance shows that proposed filters have better regularity, symmetry and less energy of the error compared with existing FBs. Finally, performance of designed filters is evaluated in image denoising application.