MIT Media Laboratory Vision and Modeling Technical Report
Appears in Subband Coding edited by John Woods Kluwer Academic Press
Chapter
Subband Transforms
y z
Eero P Simoncelli and Edward H Adelson
Vision Science Group The Media Lab oratory and
y
DepartmentofElectrical Engineering and Computer Science
z
Departmentof Brain and CognitiveScience
Massachusetts Institute of Technology
Cambridge Massachusetts
Linear transforms are the basis for manytechniques used in image pro
cessing image analysis and image co ding Subband transforms are a sub class
of linear transforms whicho er useful prop erties for these applications In
this chapter wediscuss a varietyofsubband decomp ositions and illustrate
their use in image co ding Traditionally coders based on linear transforms
are divided into twocategories transform co ders and subband co ders This
distinction is due in part to the nature of the computational metho ds used for
the twotyp es of representation
Transform co ding techniques are usually based on orthogonal linear trans
forms The classic example of suchatransform is the discrete Fourier trans
form DFT whichdecomp oses a signal into sinusoidal frequency comp o
nents Twoother examples are the discrete cosine transform DCT and the
Karhunen Lo evetransform KLT Conceptually these transforms are com
puted bytaking the inner pro duct of the nite length signal with a set of basis
functions This pro duces a set of co e cients which are then passed on to the
This work was supp orted bycontracts with the IBM Corp oration agreementdated
and DARPA Rome Airforce F C and a grantfrom the NSF IRI
The opinions expressed are those of the authors and do not necessarily representthose of
the sp onsors