Edge direction preserving image zooming: A mathematical and numerical analysis

SIAM Journal on Numerical Analysis

Volumn 39, Issue 1, 2002, Pages 1-37

  Malgouyres, F ^a   Guichard, F ^b  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b NONE

Author keywords

Fourier analysis; Image interpolation; Image reconstruction; Image restoration; Numerical approximation; Total variation; Variational methods

Indexed keywords

EID: 0035733621     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142999362286     Document Type: Article

References (30)

1. R. ACAR AND C. VOGEL, Analysis of bounded variation methods for ill-posed problems, Inverse Problems, 10 (1994), pp. 1217-1229.
2. A. ALBIOL AND J. SERRA, Morphological image enlargements, J. Visual Comm. and Image Representation, 8 (1997), pp. 367-383.
3. J. ALLEBACH AND P. W. WONG, Edge-directed interpolation, in Proceedings of the International Conference on Image Processing, Vol. 3, IEEE Press, Los Alamitos, CA, 1996, pp. 707-710.
4. E. CASAS, K. KUNISCH, AND C. POLA, Regularization by functions of bounded variation and applications to image enhancement, Appl. Math. Optim., 40 (1999), pp. 229-257.
5. V. CASELLES, J. L. LISANI, J. M. MOREL, AND G. SAPIRO, Shape preserving local histogram modification, IEEE Trans. Image Process., 8 (1999), pp. 220-230.
6. A. CHAMBOLLE AND P.-L. LIONS, Image recovery via total variation minimization and related problems, Numer. Math., 76 (1997), pp. 167-188.
7. T. F. CHAN AND P. MULET, On the convergence of the lagged diffusivity fixed method in total variation image restoration, SIAM J. Numer. Anal., 36 (1999), pp. 354-367.
8. S. DURAND, F. MALGOUYRES, AND B. ROUGÉ, Image de-blurring, spectrum interpolation and application to satellite imaging, ESAIM Control Optim. Calc. Var., 5 (2000), pp. 445-475; also available at http://www.cmla.ens-cachan.fr/~malgouy.
9. L. EVANS AND R. F. GARIEPY, Measure Theory and Fine Properties of Functions, Stud. Adv. Math., CRC Press, Boca Raton, FL, 1992.
10. F. GUICHARD AND F. MALGOUYRES, Total variation based interpolation, in Proceedings of the Ninth European Signal Processing Conference, Vol. 3, Patran, Greece, 1998, pp. 1741-1744.
11. K. ITO AND K. KUNISCH, An active set strategy based on the augmented Lagrangian formulation for image restoration, Math. Model. Numer. Anal., 33 (1999), pp. 1-21.
12. N. B. KARAYIANNIS AND A. N. VENETSNOPOULOS, Image interpolation based on variational principles, Signal Processing, 25 (1991), pp. 259-288.
13. H. LANDAU AND H. POLLAK, Prolate spheroidal wave functions, Fourier analysis and uncertainty III: The dimension of the space of essentially time and bandlimited signals, Bell System Tech. J., 41 (1962), pp. 1295-1336.
14. E. MAELAND, On the comparison of interpolation methods, IEEE Trans. Medical Imaging, 7 (1988), pp. 213-217.
15. F. MALGOUYRES, Increase in the Resolution of Digital Images: Variational Theory and Applications, Ph.D. thesis, Ecole Normale Superieure de Cachan, Cachan, France, 2000, available at http://www.cmla.ens-cachan.fr/~malgouy.
16. S. MALLAT, A Wavelet Tour of Signal Processing, Academic Press, Boston, 1998.
17. S. MATEJ, S. S. FURUIE, AND G. HERMAN, The relevance of statistically significant differences between reconstruction algorithms, IEEE Trans. Image Process., 5 (1996), pp. 554-556.
18. M. NASHED AND O. SCHERZER, Least square and bounded variation regularization with nondifferentiable functions, Numer. Funct. Anal. Optim., 19 (1998), pp. 873-901.
19. J. P. OACKLEY AND M. J. CUNNINGHAM, A function space model for digital image sampling and its application in image reconstruction, Comput. Vision Graphics Image Process., 49 (1990), pp. 171-197.
20. S. K. PARK AND R. A. SCHROWENGERDT, Image reconstruction by parametric cubic convolution, Comput. Vision Graphics Image Process., 23 (1983), pp. 258-272.
21. L. RUDIN, S. OSHER, AND E. FATEMI, Nonlinear total variation based noise removal algorithms, Phys. D, 60 (1992), pp. 259-268.
22. L. I. RUDIN, Images, Numerical Analysis of Singularities and Shock Filters, Ph.D. thesis, California Institute of Technology, Pasadena, CA, 1987.
23. W. RUDIN, Real and Complex Analysis, 3rd ed., McGraw-Hill, New York, 1987.
24. C. E. SHANNON, Communication in the presence of noise, Proceedings of the IRE, 37 (1949), pp. 10-21.
25. S. THURNHOFER AND S. K. MITRA, Edge-enhanced image zooming, Optical Engrg., 35 (1996), pp. 1862-1870.
26. M. UNSER, A. ALDROUBI, AND M. EDEN, Enlargement or reduction of digital image with minimum loss of information, IEEE Trans. Image Process., 4 (1995), pp. 247-258.
27. S. J. WERNECKE AND L. D'ADDARIO, Maximum entropy image reconstruction, IEEE Trans. Comput., c-26 (1977), pp. 351-364.
28. L. YAROSLAVSKY, Efficient algorithm for discrete sinc interpolation, Appl. Optics, 36 (1997), pp. 460-463.
29. K. YOSIDA, Functional Analysis, Springer-Verlag, Berlin, 1965.
30. A. ZYGMUND, Trigonometric Series, Cambridge University Press, Cambridge, UK, 1959.