On symmetric extensions orthogonal transforms of images, and paraunitary filter banks

摘要

Periodic or symmetric extensions are commonly used for processing images and other finite-length signals with a paraunitary filter bank (PUFB). Unlike infinite-length signals, PUFBs applied to finite-length signals will not necessarily lead to an orthogonal system. The authors show that for symmetric extensions, orthogonality is only possible for special PUFBs based on linear-phase filters. They also discuss implementation issues.