Framelets: MRA-based constructions of wavelet frames
Publication
, Journal Article
Daubechies, I; Han, B; Ron, A; Shen, Z
Published in: Applied and Computational Harmonic Analysis
January 1, 2003
We discuss wavelet frames constructed via multiresolution analysis (MRA), with emphasis on tight wavelet frames. In particular, we establish general principles and specific algorithms for constructing framelets and tight framelets, and we show how they can be used for systematic constructions of spline, pseudo-spline tight frames, and symmetric bi-frames with short supports and high approximation orders. Several explicit examples are discussed. The connection of these frames with multiresolution analysis guarantees the existence of fast implementation algorithms, which we discuss briefly as well. © 2002 Elsevier Science (USA). All rights reserved.
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Published In
Applied and Computational Harmonic Analysis
DOI
ISSN
1063-5203
Publication Date
January 1, 2003
Volume
14
Issue
1
Start / End Page
1 / 46
Related Subject Headings
- Numerical & Computational Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
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Daubechies, I., Han, B., Ron, A., & Shen, Z. (2003). Framelets: MRA-based constructions of wavelet frames. Applied and Computational Harmonic Analysis, 14(1), 1–46. https://doi.org/10.1016/S1063-5203(02)00511-0
Daubechies, I., B. Han, A. Ron, and Z. Shen. “Framelets: MRA-based constructions of wavelet frames.” Applied and Computational Harmonic Analysis 14, no. 1 (January 1, 2003): 1–46. https://doi.org/10.1016/S1063-5203(02)00511-0.
Daubechies I, Han B, Ron A, Shen Z. Framelets: MRA-based constructions of wavelet frames. Applied and Computational Harmonic Analysis. 2003 Jan 1;14(1):1–46.
Daubechies, I., et al. “Framelets: MRA-based constructions of wavelet frames.” Applied and Computational Harmonic Analysis, vol. 14, no. 1, Jan. 2003, pp. 1–46. Scopus, doi:10.1016/S1063-5203(02)00511-0.
Daubechies I, Han B, Ron A, Shen Z. Framelets: MRA-based constructions of wavelet frames. Applied and Computational Harmonic Analysis. 2003 Jan 1;14(1):1–46.
Published In
Applied and Computational Harmonic Analysis
DOI
ISSN
1063-5203
Publication Date
January 1, 2003
Volume
14
Issue
1
Start / End Page
1 / 46
Related Subject Headings
- Numerical & Computational Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics