Multiresolution analysis: Difference between revisions

Revision as of 16:13, 5 May 2016

Revision as of 03:23, 21 June 2016

Line 1:

A '''multiresolution analysis''' ('''MRA''') or '''multiscale approximation''' ('''MSA''') is the design method of most of the practically relevant [[discrete wavelet transform]]s (DWT) and the justification for the [[algorithm]] of the [[fast wavelet transform]] (FWT). It was introduced in this context in 1988/89 by [[Stephane Mallat]] and [[Yves Meyer]] and has predecessors in the [[microlocal analysis]] in the theory of [[differential equation|differential equations]]s (the ''[[ironing method]]'') and the [[pyramid (image processing)|pyramid method]]s of [[image processing]] as introduced in 1981/83 by Peter J. Burt, Edward H. Adelson and [http://www-prima.inrialpes.fr/Prima/Homepages/jlc/jlc.html James L. Crowley].

== Definition ==

A ''multiresolution analysis'' of the [[Lp space|Lebesgue space]] <math>L^2(\mathbb{R})</math> consists of a [[sequence]] of nested [[linear subspace|subspaces]]

Line 30 ⟶ 29:

is a countable complete [[orthonormal wavelet]] basis in <math>L^2(\R)</math>.

== See also ==

* [[Multiscale modeling]]

* [[Scale space]]

Line 37 ⟶ 36:

{{no footnotes|date=April 2013}}

== References ==

* {{cite book|first=Charles K.|last=Chui|title=An Introduction to Wavelets|year=1992|publisher=Academic Press|___location=San Diego|isbn=0-585-47090-1}}

* {{cite book|author1-link=Ali Akansu|first1=A.N.|last1=Akansu|first2=R.A.|last2=Haddad|title=Multiresolution signal decomposition: transforms, subbands, and wavelets|publisher=Academic Press|year=1992|isbn=978-0-12-047141-6}}

Line 46 ⟶ 45:

== External links ==

[[Category:Wavelets]]

[[Category:Time–frequency analysis]]

[[Category:Wavelets]]