Non-Recursive Wavelet Transforms in l2(Zc+)

Abstract

Today, almost all of the implementations of the discrete wavelet transforms are based on the recursive way. However, non-recursive wavelet transforms (NRWT) are more effective and more flexible. We extend the NRWT theory in lscr² (Z) and propose a new NRWT theory based on 6 different downsampling modes in lscr² (Z_c ⁺). This extending makes NRWT more practical and can be compatible with the traditional recursive wavelet transform. We study the properties of the NRWT under the 6 downsampling modes, W_-3leskles2, through the analysis of redundancy degree and point out that W_-2 is optimal and the redundancy degrees of W_-2 and W₀ are identical. The analysis of redundancy degree offers a method to choose the NRWT mode.