Neville–Lagrange wavelet family for lossless image compression

This paper presents a new wavelet family by combining the Neville filter theory and Lagrange interpolation. The filter banks of the new wavelet family are built and named as Neville–Lagrange lifting wavelet filter banks (N–LLWFBs for short). The prediction filters of N–LLWFBs are obtained by considering the signal sampling and Lagrange interpolation, and the corresponding update filters are given by using Neville filter theory. Examples are given by using this approach. The Neville–Lagrange prediction filters are obtained; causal lifting wavelet filter banks are also constructed by using this approach. Several N–LLWFBs for image compression are designed, and they are normalized in terms of the normalization conditions of the first generation wavelet filter bank. As a special example, the lifting scheme of 5/3 wavelet of JPEG2000 is obtained; it is the two-channel N–LLWFB of order 2 both dual and primal vanishing moments. Experiment results show that the performance of N–LLWFBs for image compression becomes better with the increase of their vanishing moments.