Pseudoframes for subspaees with applications

Journal of Fourier Analysis and Applications

Volumn 10, Issue 4, 2004, Pages 409-431

  Li, Shidong ^a   Ogawa, Hidemitsu ^b  

^a SAN FRANCISCO STATE UNIVERSITY   (United States)

^b TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Frames; Pseudoframes; Series expansion

Indexed keywords

EID: 4544369762     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00041-004-3039-0     Document Type: Article

References (40)

1. Albert, A. (1972). Regression and the Moor-Penrose Pseudoinverses, Academic Press.
2. Balan, R. (1999). Equivalence relations and distances between Hilbert frames, Proc. AMS, 127(8), 2353-2366.
3. Balan, R., Casazza, P., Heil, C., and Landau, Z. (2003). Deficits and excesses of frames, Adv. Comp. Math., 18, 93-116.
4. Balan, R., Casazza, P., Heil, C., and Landau, Z. (2003). Excesses of Gabor frames, Appl. Comp. Harm. Anal., 14, 87-106.
5. Balan, R., Daubechies, I., and Vaishampayan, V. (2000). The analysis and design of windowed Fourier frame based multiple description encoding schemes, IEEE Trans. Inform. Theory, 46(7), 2491-2537.
6. Benedetto, J.J. (1994). Frame decompositions, sampling, and uncertainty principle inequalities, in Wavelets: Mathematics and Applications, Benedetto, J.J. and Frazier, M.W., Eds., CRC Press Inc., Boca Raton, FL, Chapter 7.
7. Benedetto, J.J. and Li, S. (1993). Multiresolution analysis frames with applications, ICASSP'93, Minneapolis, April 26-30, III, 304-307.
8. Benedetto, J.J. and Li, S. (1994). Subband coding and noise reduction in multiresolution analysis frames, Proc. SPIE Conf. Mathematical Imaging, July, San Diego.
9. Benedetto, J.J. and Li, S. (1998). The theory of multiresolution analysis frames and applications to filter banks, Appl. Comput. Harmon. Anal., 5, 389-427.
10. Ben-Israel, A. and Greville, T.N.E. (1974). Generalized Inverses: Theory and Applications, John Wiley & Sons, p. 39.
11. Berrached, N-E. and Ogawa, H. (1994). Extended pseudo-biorthogonal bases of type O and type L, IEICE Trans. Inf. Syst., (Japan), E77-D(3), 299-305, March.
12. Berrached, N-E. and Ogawa, H. (1994). Frame and special types of extended pseudo-biorthogonal bases, Proc. SPIE'94, Wavelet Applications in Signal and Image Processing II, San Diego, 2303, 129-140, July.
13. Casazza, P.G. (2003). Private communication.
14. Christensen, O. (1995). Frames and pseudo-inverses, J. Math. Anal. Appl., 195, 401-416.
15. Cohen, A., Daubechies, I., and Feauveau, J.-C. (1992). Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math., 45, 485-560.
16. Daubechies, I. (1992). Ten Lectures on Wavelets, SIAM.
17. Daubechies, I., Grossmann, A., and Meyer, Y. (1986). Painless nonorthogonal expansions, J. Math. Phys., 27, 1271-1283.
18. Duffin, R. and Schaeffer, A. (1952). A class of nonharmonic Fourier series, Trans. Am. Math. Soc., 72, 341-366.
19. Frazier, M. and Jawerth, B. (1985). Decomposition of Besov spaces, Indiana Univ. Math. J., 34(4), 777-799.
20. Feichtinger, H.G. and Gröechenig, K. (1992). Gabor wavelets and the Heisenberg group: Gabor expansions and short time Fourier transform from the group theoretical point of view, in Wavelets: A Tutorial in Theory and Applications, Chui, C.K., Ed., Academic Press, Boston, 2, 359-398.
21. Feichtinger, H.G. and Gröechenig, K. (1992). Iterative reconstruction of multivariate band-limited functions from irregular sampling values, Siam J. Math. Anal., 23(1), 244-261.
22. Groetsch, C.W. (1977). Generalized Inverses for Linear Operators: Representation and Approximation, Marcel-Dekker, Inc., New York and Basel.
23. Heil, C. and Walnut, D. (1989). Continuous and discrete wavelet transforms, SIAM Review, 31, 628-666.
24. Li, S. (1993). The theory of frame multiresolution analysis and its applications, PhD dissertation, University of Maryland Graduate School, Baltimore, May.
25. Li, S. (1995). On general frame decompositions, Num. Funct. Anal. Optimizat., 16(9/10), 1181-1191.
26. Li, S. (2001). A theory of generalized multiresolution structure and pseudoframes of translates, J. Fourier Anal. Appl., 7(1), 23-40.
27. Li, S. (2003). Parametric biorthogonal wavelets and filterbanks via the theory of pseudoframe for subspaces, in preparation, presented at SampTA'03, Strobl, Austria, May.
28. Li, S. and Ogawa, H. (2001). Pseudo-duals of frames with applications, App. Comp. Harm. Anal., 11, 289-304.
29. Ogawa, H. (1982). Image reconstruction from projection-series expansion method equivalent to Fourier transform method, IEICE Trans. D, (In Japanese), J65-D(7), 834-841, October.
30. Ogawa, H. (1982). Image reconstruction from incomplete projections, Proc. ISMIII'82, 1st IEEE Computer Society Intl. Symp. on Medical Imaging and Image Interpretation, West Berlin, Germany, 534-539, October 26-28.
31. Ogawa, H. (1986). A unified approach to generalized sampling theorem, Proc. IEEE-IECEJ-ASJ Int. Conf. on Acoustics, Speech, and Signal Processing, 1657-1660, April.
32. Ogawa, H. (1989). A generalized sampling theorem, Electronics and Communications in Japan, 72(3), 97-105, March.
33. Ogawa, H. and Berrached, N-E. (1993). A theory of extend pseudo-biorthogonal bases, IEICE Trans. Inf. Syst., E76-D(8), 890-897, August.
34. Ogawa, H. and Berrached, N-E. (2000). EPBOBs (Extended Pseudo Biorthogonal Bases) for signal recovery, IEICE Trans. Inf. Syst., (Japan), E83-D(2), 223-232, February.
35. d), Can. J. Math., 47(5), 1051-1094.
36. d): The analysis of the analysis operator, J. Funct. Anal., 148(2),p. 408.
37. Strang, G. and Nguyen, T. (1996). Wavelets and Filter Banks, Wellesley-Cambridge Press, Wellesley, MA.
38. Unser, M. and Aldroubi, A. (1994). A general sampling theory for non-ideal acquisition devices, IEEE Trans. Signal Proc., 42(11), 2915-2925, November.
39. Vetterli, M. and Kovačević, J. (1995). Wavelets and Subband Coding, Prentice-Hall PTR, Englewood Cliffs, NJ.
40. Young, R. (1980). An Introduction to Nonharmonic Fourier Series, Academic Press, New York.