Wavelet Transforms that Map Integers to Integers Based on Lifting Scheme

The lifting scheme is a new idea of constructing wavelet filters. Its key element is to find the predict operator and the update operator. The polynomial local regression is used to find these operators in the paper. These lifting steps take integers downwardly. Then the wavelet transforms that map integers to integers are realized. The algorithm is applied to two dimensions digital image processing, and the simulation indicates that compression ratio is high with allowable distortion. The scale coefficients and wavelet coefficients are integers, thus the quantification is not needed. This brings the sigiiifican importance of the proposed algorithm for integer data compression.