Linear phase paraunitary filter bank with filters of different lengths and its application in image compression

In this paper, the theory, structure, design, and implementation of a new class of linear-phase paraunitary filter banks (LPPUFB's) are investigated. This new class of filter banks with filters of different lengths can be viewed as generalized lapped orthogonal transforms (GenLOT's) with variable-length basis functions. Our main motivation for the new transform is its application in block-transform-based image coding. Besides having all of the attractive properties of other lapped orthogonal transforms, the new transform takes advantage of its long basis functions to represent smooth signals and to reduce blocking artifacts while reserving its short basis functions for high-frequency signal components like edges and texture to reduce ringing. Two design methods are presented, each with its own set of advantages: The first is based on a direct lattice factorization, and the second enforces certain relationships between GenLOT's lattice coefficients to obtain variable-length filters. Various necessary conditions for the existence of meaningful solutions are derived and discussed in both cases. Finally, several design and image coding examples are presented to confirm the validity of the theory.