Fast implementation of orthogonal greedy algorithm for tight wavelet frames

Signal Processing

Volumn 86, Issue 3, 2006, Pages 471-479

  Petukhov, Alexander ^a  

^a UNIVERSITY OF GEORGIA   (United States)

Author keywords

Image compression; Orthogonal greedy algorithm; Wavelet frame

Indexed keywords

COMPUTER SIMULATION; IMAGE COMPRESSION; SIGNAL TO NOISE RATIO; WAVELET TRANSFORMS;

GREEDY ALGORITHMS; ORTHOGONAL GREEDY ALGORITHM; WAVELET FRAME;

ALGORITHMS;

EID: 30844451618     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2005.05.025     Document Type: Article

References (22)

1. B.K. Natarajan Sparse approximate solution to linear systems SIAM J. Comput. 24 1995 227 234
2. S.S. Chen, D.L. Donoho, and M.A. Saunders Atomic decomposition by basis pursuit SIAM Rev. 43 2001 129 159
3. R.R. Coifman, and M.V. Wickerhauser Entropy-based algorithms for best basis selection IEEE Trans. Inform. Theory 38 1992 713 718
4. R.A. DeVore, and V.N. Temlyakov Some remarks on greedy algorithms Adv. Comput. Math. 12 1996 213 227
5. S. Mallat, and Z. Zhang Matching persuits with time-frequency dictionaries IEEE Trans. Signal Process. 41 1993 3397 3415
6. V.N. Temlyakov Nonlinear methods of approximation Found. Comput. Math. 3 2003 33 107
7. V.N. Temlyakov The best n-term approximation and Greedy algorithms Adv. Comp. Math. 8 1998 249 265
8. L.F. Villemoes Best approximation with Walsh atoms Constr. Approx. 13 1997 329 355
9. R.J. Duffin, and A.C. Shaeffer A class of nonharmonic Fourier series Trans. Amer. Math. Soc. 72 1952 147 158
10. R.W. Gerchberg Super-resolution through error energy reduction Optica Acta 21 9 1974 709 720
11. A. Papoulis A new algorithm in spectral analysis and band-limited extrapolation IEEE Trans. Circuits Systems 22 9 September 1975 735 742
12. T. Hastie, R. Tibshirani, and J.H. Friedman Elements of Statistical Learning 2001 Springer New York
13. Y.C. Pati, R. Rezaiifar, P.S. Krishnaprasad, Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition, Proceedings of the 27th Annual Asilomar Conference on Signals, Systems, and Computers, 1993.
14. N.G. Kingsbury, T.H. Reeves, Iterative image coding with overcomplete complex wavelet transforms, Proceedings of the Conference on Visual Communications and Image Processing, Lugano, paper 1160, July 8-11, 2003.
15. d): the analysis of the analysis operator J. Func. Anal. 148 1997 408 447
16. C. Herley, and M. Vetterli Wavelets and recursive filter banks IEEE Trans. Signal Process. 41 1993 2536 2556
17. A. Petukhov, in: C.K. Chui, L.L. Schumaker, J. Stöckler (Eds.), Framelets with Many Vanishing Moments, Approximation Theory X: Wavelets, Splines, and Applications, 2002, pp. 425-432.
18. A. Ron, N. Stefansson, Private communication, 2001.
19. A. Cohen, I. Daubechies, and J.C. Feauveau Biorthogonal bases of compactly supported wavelets Comm. Pure Appl. Math. 45 1992 485 500
20. A. Cohen, W. Dahmen, I. Daubechies, and R. DeVore Tree approximation and encoding Appl. Comput. Harmon. Anal. 11 2001 192 226
21. A. Petukhov Construction of symmetric orthogonal bases of wavelets and tight wavelet frames with integer dilation factor Appl. Comput. Harmon. Anal. 17 2004 198 210
22. A. Petukhov Biorthogonal wavelet bases with rational masks and their applications Trudy St. Petersburg Mat. Ob. 7 1999 168 193