multiresolution analysis


A multiresolution analysis is a sequence (Vj)j of subspacesPlanetmathPlanetmath of L2() such that

  1. 1.

    (nesting) V-1V0V1

  2. 2.

    (density) spanjVj¯=L2()

  3. 3.

    (separationPlanetmathPlanetmath) jVj={0}

  4. 4.

    (scaling) f(x)Vj if and only if f(2-jx)V0

  5. 5.

    (orthonormal basisMathworldPlanetmath) there exists a function ΦV0, called a scaling function, such that the system {Φ(t-m)}m} is an orthonormal basis in V0.


Multiresolution analysis, particularly scaling functions, are used to derive wavelets. The Vj are called approximation spaces. Several choices of scaling functions may exist for a given set of approximation spaces— each determines a unique multiresolution analysis.

Title multiresolution analysis
Canonical name MultiresolutionAnalysis
Date of creation 2013-03-22 14:26:48
Last modified on 2013-03-22 14:26:48
Owner swiftset (1337)
Last modified by swiftset (1337)
Numerical id 5
Author swiftset (1337)
Entry type Definition
Classification msc 46C99
Synonym level of detail
Related topic Wavelet
Defines scaling function