Characterization of oblique dual frame pairs

Eurasip Journal on Applied Signal Processing

Volumn 2006, Issue , 2006, Pages

  Eldar, Yonina C ^a   Christensen, Ole ^b  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; SIGNAL GENERATORS; SIGNAL PROCESSING; STANDARDS;

DUAL FRAMES; FRAME OPERATOR; FRAME SETTING; HILBERT SPACE;

COMPUTATIONAL METHODS;

EID: 33746912013     PISSN: 11108657     EISSN: 16870433     Source Type: Journal    
DOI: 10.1155/ASP/2006/92674     Document Type: Article

References (34)

1. R. J. Duffin A. C. Schaeffer A class of nonharmonic Fourier series. Transactions of the American Mathematical Society 72 1952 341 366
2. R. M. Young An Introduction to Nonharmonic Fourier Series. Academic Press New York, NY, USA 1980
3. I. Daubechies Ten Lectures on Wavelets. SIAM Philadelphia, Pa, USA 1992
4. O. Christensen An Introduction to Frames and Riesz Bases. Birkhäuser Boston, Mass, USA 2003
5. J. J. Benedetto C. K. Chui Irregular sampling and frames. Wavelets: A Tutorial in Theory and Applications CRC Press Boca Raton, Fla, USA 1992 445 507
6. A. Aldroubi K. Gröchenig Non-uniform sampling and reconstruction in shift-invariant spaces. Siam Review 43 2001 4 585 620
7. C. E. Heil D. F. Walnut Continuous and discrete wavelet transforms. SIAM Review 31 1989 4 628 666
8. I. Daubechies The wavelet transform, time-frequency localization and signal analysis. IEEE Trans. Inform. Theory 36 1990 5 961 1005
9. N. J. Munch Noise reduction in tight Weyl-Heisenberg frames. IEEE Trans. Inform. Theory 38 1992 2 608 616
10. Y. C. Eldar Sampling with arbitrary sampling and reconstruction spaces and oblique dual frame vectors. Journal of Fourier Analysis and Applications 9 2003 1 77 96
11. Z. Cvetković M. Vetterli Overcomplete expansions and robustness. Proc. IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (TFTS '96) Paris, France 1996 325 328
12. V. K. Goyal M. Vetterli N. T. Thao Quantized overcomplete expansions in N: analysis, synthesis, and algorithms. IEEE Trans. Inform. Theory 44 1998 1 16 31
13. Y. C. Eldar H. Bölcskei Geometrically uniform frames. IEEE Trans. Inform. Theory 49 2003 4 993 1006
14. Z. Cvetković Overcomplete expansions for digital signal processing. University of California Berkeley, Calif, USA December 1995
15. Z. Cvetković M. Vetterli Oversampled filter banks. IEEE Trans. Signal Processing 46 1998 5 1245 1255
16. H. Bölcskei Oversampled filter banks and predictive subband coders. Vienna University of Technology Vienna, Austria November 1997
17. H. Bölcskei F. Hlawatsch H. G. Feichtinger Frame-theoretic analysis of oversampled filter banks. IEEE Trans. Signal Processing 46 1998 12 3256 3268
18. P. J. S. G. Ferreira J. S. Byrnes Mathematics for multimedia signal processing II - discrete finite frames and signal reconstruction. Signal Processing for Multimedia IOS Press Amsterdam, The Netherlands 1999 35 54
19. Y. C. Eldar G. D. Forney Jr. Optimal tight frames and quantum measurement. IEEE Trans. Inform. Theory 48 2002 3 599 610
20. Y. C. Eldar J. J. Benedetto A. I. Zayed Sampling without input constraints: Consistent reconstruction in arbitrary spaces. Sampling, Wavelets and Tomography Birkhäuser Boston, Mass, USA 2004 33 60
21. T. Werther Y. C. Eldar General framework for consistent sampling in Hilbert spaces. to appear in International Journal of Wavelets, Multiresolution and Information Processing
22. O. Christansen Y. C. Eldar Oblique dual frames and shift-invariant spaces. Applied and Computational Harmonic Analysis 17 2004 1 48 68
23. O. Christansen Y. C. Eldar Generalized shift-invariant systems and frames for sub-spaces. submitted to Applied and Computational Harmonic Analysis
24. S. Li H. Ogawa Pseudoframes for subspaces with applications. Journal of Fourier Analysis and Applications 10 2004 4 409 431
25. N. K. Subbanna Y. C. Eldar Efficient Gabor expansion using non minimal dual Gabor windows. Proc. 11th IEEE International Conference on Electronics, Circuits and Systems (ICECS '04) Tel-Aviv, Israel 2004 650 653
26. N. K. Subbanna Y. C. Eldar A fast algorithm for calculating the dual Gabor window with integer oversampling. Proc. 23rd IEEE Convention of Electrical and Electronics Engineers in Israel (IEEEI '04) Tel-Aviv, Israel 2004 368 371
27. T. Werther Y. C. Eldar N. K. Subbana Dual Gabor frames: theory and computational aspects. to appear in IEEE Trans. Signal Processing, October 2004
28. H. Heuser Functional Analysis. John Wiley & Sons New York, NY, USA 1982
29. W.-S. Tang Oblique projections, biorthogonal Riesz bases and multiwavelets in Hilbert space. Proceedings of the American Mathematical Society 128 2000 2 463 473
30. G. H. Golub C. F. Van Loan Matrix Computations. 3rd Johns Hopkins University Press Baltimore, Md, USA 1996
31. S. Li On general frame decompositions. Numerical Functional Analysis and Optimization 16 1995 9-10 1181 1191
32. O. Christensen B. Deng C. Heil Density of Gabor frames. Applied and Computational Harmonic Analysis 7 1999 3 292 304
33. J. Benedetto S. Li The theory of multiresolution analysis frames and applications to filter banks. Applied and Computational Harmonic Analysis 5 1998 4 389 427
34. M. Unser A. Aldroubi A general sampling theory for nonideal acquisition devices. IEEE Trans. Signal Processing 42 1994 11 2915 2925