OPTIMAL ADAPTIVE WAVELET TRANSFORMS WITHOUT USING EXTRA ADDITIONAL INFORMATION

Guangchun Gao, Kai Xiong, Shengying Zhao, Cui Zhang

School of Information Science & Electronic Engineering, Zhejiang University City College, Hangzhou, China, 310015

 Wavelet transforms via lifting scheme provides a general and an adaptive flexible tool for the construction of wavelet decompositions and perfect reconstruction filter banks. According to the construction of the lifting wavelet transforms, the optimal filter design method for the adaptive update wavelet transform is proposed by the authors. The optimal update filter coefficients can be acquired based on the Minimum Mean Square Error Criteria (MMSE) in the algorithm. In prediction process, take the case of LeGall 5/3 wavelet, we propose an adaptive version of this scheme that it allows perfect reconstruction without any overhead cost for the smooth signals with the jumps. Compare with other wavelet transform scheme, simulation results show that optimal adaptive wavelet transform proposed by this paper can achieve the detail signals being zero (or almost zero) at big probability and the better linear approximation for the piecewise continuous signal.