$M$-Channel Nonlinear Phase Filter Banks in Image Compression: Structure, Design, and Signal Extension
This paper describes a transform coding technique based on M-channel perfect reconstruction filter banks with a nonlinear phase. In contrast with linear-phase filter banks, the nonlinearity provides an extra degree of freedom that can be used to design a more efficient transform. We present new lattice structures of paraunitary and perfect reconstruction (biorthogonal) filter banks, which can be implemented with a lower computational complexity and/or represented by a few free parameters, through the decomposition of the lattice blocks and the displacement across the delay block. We further discuss a smooth extension method for nonlinear-phase filter banks to obtain a nonexpansive transform. The promise of our proposed approaches is demonstrated through several design examples, extended signals and compression results