Single-rate calculation of overcomplete discrete wavelet transforms for scalable coding applications

Abstract

A number of emerging resolution-scalable image and video cdeob algorithms haverecbWzq shown very promising performanc due to the use ofovercTb;WII wavelet representations. In theseapplicWqqb;W theovercWBb;WI disccW wavelet transform (ODWT) is derived starting from the cbOzBBfib;W..xBbc subbands of the DWT(cbTqWqI representation) of acIIBO. decO.b;Ox..T (resolution) level. ThisprocOxT whic is acfixqIb;Ox..Tbcccx.. DWT (CODWT), is used for wavelet domain operations that require shiftinvariancb Speciancb; both theencTTT and decbTx independentlycdepende theovercBIb;Ofi representation at the bestactbWTW possible, given thecbTqzIqb;O sampled subbands of acIOx.x resolution level. IncbOW.Ox to thecebOBzz. approac for performing the CODWT,whic is a multi-rate clti;rateb scti; that requires therecWzWzb;OTfiI of the input spatial-domain signal, in this paper we propose a new, single-rate cngle;rate scngle whic is formalized for the generalcne of an ar itrarydecybTWzfiBb; (resolution) level. Based on derived symmetry properties, a simple implementationstrucmen of the proposed approac provides interesting tradeoffs for the requiredmultipliczIfib udget incWIO.Bb;O to thecbWBTTOb;OI approacO This leads to a cxfi.b;O.OWTbc le solution that fits the versatile requirements ofscWW lecbWfiB environments. The use of the proposed single-rate cgle-rateb scgle of the CODWT is demonstrated in several image and video coding systems