Pacific-Asia Workshop on Computational Intelligence and Industrial Application, IEEE (2008)
Dec. 19, 2008 to Dec. 20, 2008
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 l^2 (Z) and propose a new NRWT theory based on 6 different downsampling modes in l^2 (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_(-3≤k≤2), through the analysis of redundancy degree and point out that W_(-2) is optimal and the redundancy degrees of W_(-2) and W_0 are identical. The analysis of redundancy degree offers a method to choose the NRWT mode.
Li Xiaoxin, Qi Deyu, Qian Zhengping, "Non-Recursive Wavelet Transforms in l2(Zc+)", Pacific-Asia Workshop on Computational Intelligence and Industrial Application, IEEE, vol. 01, no. , pp. 982-986, 2008, doi:10.1109/PACIIA.2008.45