文档介绍：TO APPEAR IN IEEE TRANSA CTIONS ON IMA GE PR OCESSING, 1997. 100
AW a v elet-Based Analysis of F ractal Image
Compression
Geo rey M. Da vis, Memb er, IEEE
A bstr act |Wh y do es fractal pression w ork?
[1] and b y Fisher in [7]. Throughout this pap er, when w e
What is the implicit image mo del underlying fractal blo c k
refer to fractal blo c k co ders, w e will b e referring to suc h
co ding? Ho w can w ec haracterize the t yp es of images for
Jacquin-st yle sc hemes. The second problem is to nd fast
whic hfractalbloc k co ders will w ork w ell? These are the
and e ectiv e algorithms for asso ciating a giv en image to a
cen tral issues w e address. W ein tro duce a new w a v elet-
based framew ork for analyzing blo c k-based pres-
con traction map of whic h the image is an appro ximate xed
sion sc hemes. Within this framew ork w e are able to dra w
p oin t[8] [9]. The third problem is to analyze the con v er-
up on insigh ts from the w ell-established transform co der
gence prop erties of v arious families of maps and to establish
paradigm in order to address the issue of wh y fractal blo c k
co ders w ork. W e sho w that fractal blo c k co ders of the
error b ounds for deco ded images[10] [11].
form in tro duced b y Jacquin[1] are a Haar w a v elet subtree
In this pap er w e address the issues of nding e ec-
quan tization sc heme. W e examine a generalization of this
tiv e famili es of maps and con v ergence prop erties of fractal
sc heme to smo oth w a v elets with additional v anishing mo-
sc hemes. More imp ortan tly ,w e address some m uc hmore
men ts. The p erformance of our generalized co der pa-
rable to the b est results in the literature for a Jacquin-st yle
fundamen tal questions. First and foremost, w e seek to ex-
co ding sc heme. Our w a v elet framew ork giv es new insigh t
plain why pression w orks. T o w ard this end, w e
in to the con v ergence prop erties of fractal blo c k co