Shift-invariant spaces from rotation-covariant functions

Applied and Computational Harmonic Analysis

Volumn 25, Issue 2, 2008, Pages 240-265

  Forster, Brigitte ^b,c   Blu, Thierry ^a   Van De Ville, Dimitri ^a   Unser, Michael ^a  

^a EPFL   (Switzerland)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^c INSTITUTE OF EPIDEMIOLOGY   (Germany)

Author keywords

Complex wavelets; Multiresolution; Riesz basis; Rotation covariance; Scaling functions; Shift invariant spaces; Two scale relation

Indexed keywords

MULTIRESOLUTION (MR); SHIFT INVARIANT; SHIFT INVARIANT SPACES;

ROTATION;

EID: 48349134392     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2007.11.002     Document Type: Article

References (19)

1. Mallat S. A Wavelet Tour of Signal Processing (1997), Academic Press
2. Wirtinger W. Zur formalen Theorie der Funktionen von mehr komplexen Veränderlichen. Math. Ann. 97 1 (1927) 357-375
3. Remmert R. Theory of Complex Functions (1991), Springer
4. Walz G. Spline-Funktionen im Komplexen (1991), BI-Wiss.-Verl.
5. Schwartz L. Théorie des Distributions (1998), Hermann reprint, original of 1966
6. Zemanian A.H. Distribution Theory and Transform Analysis (1987), Dover
7. Micchelli C.A., Rabut C., and Utreras F.I. Using the refinement equation for the construction of pre-wavelets. III. Elliptic splines. Numer. Algorithms 1 (1991) 331-352
8. Wojtaszczyk P. A Mathematical Introduction to Wavelets. London Math. Soc. Student Texts vol. 37 (1997), Cambridge University Press
9. Rabut C. Elementary m-harmonic cardinal B-splines. Numer. Algorithms 2 (1992) 39-62
10. Rabut C. High level m-harmonic cardinal B-splines. Numer. Algorithms 2 (1992) 63-84
11. Kounchev O. Multivariate Polysplines: Applications to Numerical and Wavelet Analysis (2001), Academic Press
12. Van De Ville D., Blu T., and Unser M. Isotropic polyharmonic B-splines: Scaling functions and wavelets. IEEE Trans. Image Process. 14 11 (2005) 1798-1813
13. d). Trans. Amer. Math. Soc. 341 (1994) 787-806
14. Louis A.K., Maaß P., and Rieder A. Wavelets: Theorie und Anwendung (1994), Teubner Verlag, Stuttgart
15. Bacchelli B., Bozzini M., Rabut C., and Varas M.-L. Decomposition and reconstruction of multidimensional signals using polyharmonic pre-wavelets. Appl. Comput. Harmon. Anal. 18 (2005) 282-299
16. n. IEEE Trans. Inform. Theory 38 (1992) 533-555
17. n. IEEE Trans. Inform. Theory 38 (1992) 556-568
18. Daubechies I. Ten Lectures on Wavelets. CBMS-NSF Regional Conf. Series in Appl. Math. (1992), SIAM
19. Feilner M., Van De Ville D., and Unser M. An orthogonal family of quincunx wavelets with continuously adjustable order. IEEE Trans. Image Process. 14 4 (2005) 499-510