Title :
Multiresolution analysis. Haar bases, and self-similar tilings of R/sup n/
Author :
Grochenig, K. ; Madych, W.R.
Author_Institution :
Dept. of Math., Connecticut Univ., Storrs, CT, USA
fDate :
3/1/1992 12:00:00 AM
Abstract :
Orthonormal bases for L/sup 2/(R/sup n/) are constructed that have properties that are similar to those enjoyed by the classical Haar basis for L/sup 2/(R). For example, each basis consists of appropriate dilates and translates of a finite collection of ´piecewise constant´ functions. The construction is based on the notion of multiresolution analysis and reveals an interesting connection between the theory of compactly supported wavelet bases and the theory of self-similar tilings.<>
Keywords :
signal processing; transforms; Haar basis; compactly supported wavelet bases; multiresolution analysis; orthonormal bases; self-similar tilings; signal analysis; Argon; Eigenvalues and eigenfunctions; Erbium; Fractals; Lattices; Multiresolution analysis; Wavelet analysis;
Journal_Title :
Information Theory, IEEE Transactions on
