Fast local reconstruction methods for nonuniform sampling in shift-invariant spaces

SIAM Journal on Matrix Analysis and Applications

Volumn 24, Issue 4, 2003, Pages 899-913

  Gröchenig, Karlheinz ^a   Schwab, Harald ^b  

^a UNIVERSITY OF CONNECTICUT   (United States)

^b UNIVERSITY OF VIENNA   (Austria)

Author keywords

Banded matrix; Data segmentation; Denoising; Localization; Nonuniform sampling; Shift invariant space

Indexed keywords

EID: 0142231454     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479802409067     Document Type: Article

References (17)

1. A. ALDROUBI AND K. GRÖCHENIG, Nonuniform sampling and reconstruction in shift-invariant spaces, SIAM Rev., 43 (2001), pp. 585-620.
2. A. ALDROUBI AND K. GRÖCHENIG, Beurling-Landau-type theorems for non-uniform sampling in shift invariant spline spaces, J. Fourier Anal. Appl., 6 (2000), pp. 93-103.
3. M.D. BUHMANN, Radial basis functions, in Acta Numerica, 2000, Cambridge University Press, Cambridge, UK, 2000, pp. 1-38.
4. P. CRAVEN AND G. WAHBA, Smoothing noisy data with spline functions. Estimating the correct degree of smoothing by the method of generalized cross-validation, Numer. Math., 31 (1978/79), pp. 377-403.
5. I. DAUBECHIES, Ten Lectures on Wavelets, SIAM, Philadelphia, PA, 1992.
6. d), J. Funct. Anal., 119 (1994), pp. 37-78.
7. S. DEMKO, W.F. Moss, AND P.W. SMITH, Decay rates for inverses of band matrices, Math. Comp., 43 (1984), pp. 491-499.
8. R.J. DUFFIN AND A.C. SCHAEFFER, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72 (1952), pp. 341-366.
9. H.G. FEICHTINGER, K. GRÖCHENIG, AND T. STROHMER, Efficient numerical methods in non-uniform sampling theory, Numer. Math., 69 (1995), pp. 423-440.
10. G.H. GOLUB AND C.F. VAN LOAN, Matrix Computations, 3rd ed., Johns Hopkins University Press, Baltimore, MD, 1996.
11. K. GRÖCHENIG, Acceleration of the frame algorithm, IEEE Trans. Signal Process., 41 (1993), pp. 3331-3340.
12. M.F. HUTCHINSON AND F.R. DE HOOG, Smoothing noisy data with spline functions, Numer. Math., 47 (1985), pp. 99-106.
13. S. JAFFARD, Propriétés des matrices "bien localisées" près de leur diagonale et quelques applications, Ann. Inst. H. Poincaré Anal. Non Linéaire, 7 (1990), pp. 461-476.
14. A.J.E.M. JANSSEN, The Zak transform and sampling theorems for wavelet subspaces, IEEE Trans. Signal Process., 41 (1993), pp. 3360-3365.
15. R.-Q. JIA, Stability of the shifts of a finite number of functions, J. Approx. Theory, 95 (1998), pp. 194-202.
16. L.L. SCHUMAKER, Spline Functions: Basic Theory, Pure Appl. Math, Wiley-Interscience, New York, 1981.
17. G. WAHBA, Spline Models for Observational Data, SIAM, Philadelphia, PA, 1990.