Scaling and wavelet functions generating from complementary filter banks

Abstract

We present two-dimensional (2D) complementary filter (CF) banks and a signal processing technique for image processing that can be used to generate scaling and wavelet functions. The 2D multirate signal processing theory and complementary filters properties are the base of CF banks design. Procedures to design quincunx, rectangular and circular complementary filters for alias free decimation are shown. The CF banks and wavelet representation are related and a consistent set of wavelet and scaling functions are developed. The region of support of scaling and wavelet functions can be found in each resolution level for different types of sampling. We show that quincunx sampling has two mother wavelets, since the region of support changes shape with the resolution levels. Examples of scaling and wavelet functions are shown.