Smooth extension for nonexpansive wavelet decomposition of finite length signals

In transform-based image coding, the periodic extension has the disadvantage that it might introduce high frequency components due to the artificial discontinuities at the signal boundaries. On the other hand, the symmetric extension can´t be applied to the two-channel orthogonal filter bank because linear phase is not possible. This paper describes a smooth extension method, which provides the symmetric decimated outputs of the analysis filters at the boundary, for the two-channel orthogonal filter bank to obtain nonexpansive subband signals. Then, extended signal has the flexibility under the nonexpansive condition. Therefore we can calculate the smooth extended signal by singular value decomposition. Finally, several image coding and extended signal examples are shown to confirm the validity of the proposed approach.