Redundancy in non-orthogonal transforms

Abstract

Compression efficiency is mainly driven by redundancy of the overcomplete set of functions chosen for non-orthogonal signal decompositions. Redundancy is an important criteria in the design of dictionaries, whose size only provides a first indication without however taking into account the distribution of the atoms. This paper provides a new formulation for the structural redundancy of an overcomplete set of functions. The structural redundancy factor directly drives the energy compaction properties of non-orthogonal transforms in frame expansion or matching pursuit.