Department of Mathematical Modelling

Technical University of Denmark Building 321/305 DK-2800 Lyngby Denmark

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Fast 2D wavelet transform of circulant matrices

Ole Møller Nielsen

For a copy of this paper, either

• view a full text copy of this paper
• or contact omni@imm.dtu.dk

Abstract

Circulant matrices arise from a number of problems in numerical analysis such as partial differential equations with periodic boundary conditions and problems involving periodic convolution. It has recently been suggested that one may benefit from treating such problems using wavelets.

In this report we will describe the 2D wavelet transform of a circulant matrix. We will show that this can be done in a computationally efficient way and that the transformed matrix can be represented using very few elements in a suitable data structure. Using this structure we describe an efficient algorithm for computing the matrix-vector product in the wavelet domain.

IMM Technical Report 8, 1997

Last modified May 15, 1997

For further information, please contact, Finn Kuno Christensen, IMM, Bldg. 321, DTU
Phone: (+45) 4588 1433. Fax: (+45) 4588 2673, E-mail: fkc@imm.dtu.dk

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