Smooth signal extension for M-channel paraunitary filterbanks and its application to image coding

In the transform-based image coding, the symmetric extension is important to obtain subband signals effectively without increasing the total number of signal. However in the case of the symmetric extension, subband filters have to be (anti-)symmetric. This means that the linear phase property is strict constraint on filters' impulse response for the symmetric extension. For the other method of the signal extension, the periodic extension is implemented. While it can be applied to any filters, it introduces artificial discontinuities at the signal boundaries. In this paper, we present a smooth extension for M-channel filterbanks to implement nonexpansive decomposition. First, we derive a condition for solving the coefficient expansion problem. Second, we calculate a smooth extended signal under the condition by singular value decomposition. Finally, we design 8 channel 16 tap paraunitary filterbank using lattice structure, and several image coding and extended signal examples are shown to confirm the validity of the proposed approach.