Superfast Wavelet Transform Using Quantics-TT Approximation. I. Application to Haar Wavelets
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and
Abstract
We propose a superfast discrete Haar wavelet transform (SFHWT) as
well as its inverse, using the low-rank Quantics-TT (QTT) representation for
the Haar transform matrices and input-output vectors. Though the Haar matrix
itself does not have a low QTT rank approximation, we show that factor matrices
used at each step of the traditional multilevel Haar wavelet transform
algorithm have explicit QTT representations of low rank.
The SFHWT applies to a vector representing a signal sampled on a uniform grid
of size
The first author would like to thank Dr. Venera Khoromskaia (Max-Planck-Institute for Mathematics in the Sciences, Leipzig) for useful comments on the presentation. The second author was supervised by Prof. B. Khoromskij during an internship work at Max-Planck-Institute for Mathematics in the Sciences, Leipzig, and by Prof. P. Oswald at Jacobs University, Bremen, Germany.
© 2014 by De Gruyter
Articles in the same Issue
- Frontmatter
- Error Analysis for the Finite Element Approximation of Transmission Eigenvalues
- Space-Time Residual-Based A Posteriori Estimators for the A−ϕ Magnetodynamic Formulation of the Maxwell System
- An Arbitrary-Order and Compact-Stencil Discretization of Diffusion on General Meshes Based on Local Reconstruction Operators
- Finite Volume Methods for Well-Driven Flows in Anisotropic Porous Media
- Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor
- Adaptive Nonconforming Finite Element Approximation of Eigenvalue Clusters
- Superfast Wavelet Transform Using Quantics-TT Approximation. I. Application to Haar Wavelets
- On Two Optimal Control Problems for Magnetic Fields
Articles in the same Issue
- Frontmatter
- Error Analysis for the Finite Element Approximation of Transmission Eigenvalues
- Space-Time Residual-Based A Posteriori Estimators for the A−ϕ Magnetodynamic Formulation of the Maxwell System
- An Arbitrary-Order and Compact-Stencil Discretization of Diffusion on General Meshes Based on Local Reconstruction Operators
- Finite Volume Methods for Well-Driven Flows in Anisotropic Porous Media
- Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor
- Adaptive Nonconforming Finite Element Approximation of Eigenvalue Clusters
- Superfast Wavelet Transform Using Quantics-TT Approximation. I. Application to Haar Wavelets
- On Two Optimal Control Problems for Magnetic Fields
