Linear-phase perfect reconstruction filter bank: lattice structure, design, and application in image coding

A lattice structure for an M-channel linear-phase perfect reconstruction filter bank (LPPRFB) based on the singular value decomposition (SVD) is introduced. The lattice can be proven to use a minimal number of delay elements and to completely span a large class of LPPRFBs: all analysis and synthesis filters have the same FIR length, sharing the same center of symmetry. The lattice also structurally enforces both linear-phase and perfect reconstruction properties, is capable of providing fast and efficient implementation, and avoids the costly matrix inversion problem in the optimization process. From a block transform perspective, the new lattice can be viewed as representing a family of generalized lapped biorthogonal transform (GLBT) with an arbitrary number of channels M and arbitrarily large overlap. The relaxation of the orthogonal constraint allows the GLBT to have significantly different analysis and synthesis basis functions, which can then be tailored appropriately to fit a particular application. Several design examples are presented along with a high-performance GLBT-based progressive image coder to demonstrate the potential of the new transforms.