Content deleted Content added
Reverse https://en.wikipedia.org/w/index.php?title=Multiresolution_analysis&diff=prev&oldid=1264288719 due to LLM content. Tag: section blanking |
|||
| (4 intermediate revisions by 4 users not shown) | |||
Line 1:
{{Short description|Design method of discrete wavelet transforms}}
{{Distinguish|Multiple-scale analysis}}
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]]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].
Line 5 ⟶ 6:
A multiresolution analysis of the [[Lp space|Lebesgue space]] <math>L^2(\mathbb{R})</math> consists of a [[sequence]] of nested [[linear subspace|subspaces]]
::<math>\{0\}\subset \dots\subset V_1\subset V_0\subset V_{-1}\subset\dots\subset V_{-n}\subset V_{-(n+1)}\subset\dots\subset L^2(\R)</math>
that satisfies certain [[self-similarity]] relations in time-space and scale-frequency, as well as [[Complete metric space|completeness]] and regularity relations.
| |||