Abstract
Frame multiresolution analysis is just one way to construct wavelet frames via multiscale techniques. We already mentioned in Section 17.3 that the conditions can be weakened further, and the purpose of this chapter is to show how one can still construct frames.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Benedetto, J., Treiber, O.: Wavelet frames: multiresolution analysis and extension principles. In: Debnath, L. (ed.) Wavelet Transforms and Time-Frequency Signal Analysis, pp. 1–36. Birkhäuser, Boston (2001)
Cai, J.F., Osher, S., Shen, Z.: Split Bregman methods and frame based image restoration. Multiscale Model. Simul. 8, 337–369 (2009)
Cai, J.F., Dong, B., Osher, S., Shen, Z.: Image restoration: total variation, wavelet frames, and beyond. J. Am. Math. Soc. 25, 1033–1089 (2012)
Charina, M., Putinar, M., Scheiderer, C., Stöckler, J.: An algebraic perspective on multivariate tight wavelet frames. Constr. Approx. 38, 253–276 (2013)
Charina, M., Putinar, M., Scheiderer, C., Stöckler, J.: An algebraic perspective on multivariate tight wavelet frames II. Appl. Comput. Harmon. Anal. 39(2), 185–213 (2015)
Chui, C., He, W.: Compactly supported tight frames associated with refinable functions. Appl. Comput. Harmon. Anal. 8, 293–319 (2000)
Chui, C., He, W., Stöckler, J.: Compactly supported tight and sibling frames with maximum vanishing moments. Appl. Comput. Harmon. Anal. 13(3), 226–262 (2002)
Chui, C., He, W., Stöckler, J.: Nonstationary tight wavelet frames I. Bounded intervals. Appl. Comput. Harmon. Anal. 17(2), 141–197 (2004)
Chui, C., He, W., Stöckler, J.: Nonstationary tight wavelet frames II. Unbounded intervals. Appl. Comput. Harmon. Anal. 18(1), 25–66 (2005)
Daubechies, I., Han, B.: The canonical dual of a wavelet frame. Appl. Comput. Harmon. Anal. 12(3), 269–285 (2002)
Daubechies, I., Han, B., Ron, A., Shen, Z.: Framelets: MRA-based constructions of wavelet frames. Appl. Comp. Harm. Anal. 14(1), 1–46 (2003)
Han, B., Mo, Q.: Tight wavelet frames generated by three symmetric B-spline functions with high vanishing moments. Proc. Am. Math. Soc. 132(1), 77–86 (2003)
Han, B., Mo, Q.: Multiwavelet frames from refinable function vectors. Adv. Comput. Math. 18, 211–245 (2003)
Han, B., Mo, Q.: Symmetric MRA tight wavelet frames with three generators and high vanishing moments. Appl. Comput. Harmon. Anal. 18, 67–93 (2005)
Jiang, Q.T.: Parametrizations of masks for tight affine frames with two symmetric/antisymmetric generators. Adv. Comput. Math. 18, 247–268 (2003)
Petukhov, A.: Explicit construction of framelets. Appl. Comput. Harmon. Anal. 11, 313–327 (2001)
Petukhov, A.: Symmetric framelets. Constr. Approx. 19, 309–328 (2003)
Ron, A., Shen, Z.: Affine systems in \(L_{2}(\mathbb{R}^{d})\): the analysis of the analysis operator. J. Funct. Anal. 148, 408–447 (1997)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Christensen, O. (2016). Wavelet Frames via Extension Principles. In: An Introduction to Frames and Riesz Bases. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-25613-9_18
Download citation
DOI: https://doi.org/10.1007/978-3-319-25613-9_18
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-25611-5
Online ISBN: 978-3-319-25613-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)