Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-22T20:02:38.598Z Has data issue: false hasContentIssue false
  • English
  • Français

Image deblurring, spectrum interpolation and application to satellite imaging

Published online by Cambridge University Press:  15 August 2002

Sylvain Durand ,
François Malgouyres  and
Bernard Rougé
Sylvain Durand
Affiliation:
CMLA, ENS Cachan, 61 avenue du président Wilson, 94235 Cachan Cedex, France; [email protected]. & [email protected]. LAMFA, Université de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens Cedex 1, France.
François Malgouyres
Affiliation:
CMLA, ENS Cachan, 61 avenue du président Wilson, 94235 Cachan Cedex, France; [email protected]. & [email protected].
Bernard Rougé
Affiliation:
CNES, DGAT/SH/QTIS, 18 avenue E. Belin, 31401 Toulouse Cedex 4, France; [email protected].
Get access

Abstract

This paper deals with two complementary methods in noisy image deblurring: a nonlinear shrinkage of wavelet-packets coefficients called FCNR and Rudin-Osher-Fatemi's variational method. The FCNR has for objective to obtain a restored image with a white noise. It will prove to be very efficient to restore an image after an invertible blur but limited in the opposite situation. Whereas the Total Variation based method, with its ability to reconstruct the lost frequencies by interpolation, is very well adapted to non-invertible blur, but that it tends to erase low contrast textures. This complementarity is highlighted when the methods are applied to the restoration of satellite SPOT images.

Keywords

Image restorationdeblurringwavelet-packetsTotal Variationspectrum interpolation.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 5 , 2000 , pp. 445 - 475
Copyright
© EDP Sciences, SMAI, 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Acart, R. and Vogel, C., Analysis of bounded variation methods for ill-posed problems. Inverse Problems 10 (1994) 1217-1229.
H.C. Andrews and B.R. Hunt, Digital signal processing. Tech. Englewood Cliffs, NJ: Prentice-Hall (1977).
S.M. Berman, Sojournes and Extremes os Stochastic Processes. Wadsworth, Reading, MA (1989).
A. Cohen, R. De Vore, P. Petrushev and H. Xu, Nonlinear Approximation and the Space $BV({\mathbb R}^2)$ (preprint).
V. Caselles, J.L. Lisani, J.M. Morel and G. Sapiro, Shape Preserving Local Histogram Modification. IEEE Trans. Image Process. 8 (1999).
A. Chambolle, R.A. De Vore, N. Lee and B.J. Lucier, Nonlinear Wavelet Image Processing: Variational Problems, Compression and Noise Removal through Wavelet Shrinkage. Preprint CEREMADE No. 9728, September 1997, short version in: IEEE Trans. Image Process. 7 (1998) 319-335.
A. Chambolle and P.L. Lions, Restauration de données par minimisation de la variation Total et variantes d'ordre supérieur, in Proc. of GRETSI. Juan-les-Pins, France (1995).
Chambolle, A. and Lions, P.L., Image recovery via Total Variation minimisation and related problems. Numer. Math. 76 (1997) 167-188. IEEE Trans. Image Process. CrossRef
R.H. Chan, T.F. Chan and C Wong, Cosine Transform Based Preconditioners for Total Variation Deblurring. UCLA Math Department CAM Report 95-23 (1995).
R.R. Coifman and D.L. Donoho, Translation-invariant de-noising. Technical Report 475, Standford University (1995).
R.R. Coifman, Y. Meyer and M.V. Wickerhauser, Wavelet analysis and signal processing. In Wavelets and their Applications, edited by B. Ruskai et al., Boston, Jones and Barlett (1992) 153-178.
G. Demoment, Image reconstruction and restoration: Overview of Common Estimation Structures and Problems. IEEE Trans. Acoust. Speech Signal Process. 37 (1989).
D. Donoho and I.M. Johnstone, Minimax Estimation via wavelet shrinkage. Tech. Report, Dept. of Stat., Stanford Univ. (1992).
Donoho, D.L. and Johnstone, I.M., Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 (1994) 425-455. CrossRef
L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions. Studies in advanced mathematics, CRS Press Inc. (1992).
F. Guichard and F. Malgouyres, Total Variation Based interpolation, in Proc. of European Signal Processing Conference (EUSIPCO-98), Vol. 3 (1998) 1741-1744.
I.M. Johnstone and B.W. Silverman, Wavelet threshold estimators for data with correlated noise. Technical report, Standford University (1994).
T. Kailath, A View of Three Decades of Linear Filtering Theory. IEEE Trans. Inform. Theory IT20 (1974).
J. Kalifa, Restauration minimax et déconvolution dans un base d'ondelettes miroirs. Thèse, École Polytechnique (1999).
J. Kalifa, S. Mallat and B. Rougé, Restauration d'images par paquets d'ondelettes. 16e Colloque GRETSI (1997).
J. Kalifa, S. Mallat and B. Rougé, Image Deconvolution in Mirror Wavelet Bases. IEEE, ICIP'98.
H.J. Landau and H.O. Pollak, Prolate Speroidal Wave Functions, Fourier Analysis and Uncertainty -III: The Dimension of the Space of Essentially Time and Band-Limited Signals. The Bell systeme technical Journal (1962).
Lindenbaum, M., Fischer, M. and Bruckstein, A., Gabor's, On contribution to image enhancement. PR. 27 (1994) 1-8.
S. Mallat, A theory for multiresolution signal decomposition: The wavelet representation. IEEE Trans. Patern Analysis and Machine Intelligence II (1989).
S. Mallat, A Wavelet Tour of Signal Processing. Academic Press (1998).
Y. Meyer, Ondelettes et opérateurs. Hermann (1990) Tome 1.
Y. Meyer, Les ondelettes, algorithmes et applications. Armand Colin (1992).
M. Nikolova, Local strong homogeneity of a regularized estimator. SIAM (to appear).
B. Rougé, Remarks about space-frequency and space-scale to clean and restore noisy images in satellite frameworks. Progress in wavelets and applications, edited by Y.Meyer and S. Roques Frontières. Gif-sur-Yvette 1993 (Proceedings Toulouse conference).
B. Rougé, Fixed Chosen Noise Restauration (FCNR). IEEE 95 Philadelphia (U.S.A.).
Rudin, L., Osher, S. and Fatemi, E., Nonlinear Total Variation based noise removal algorithms. Physica D 60 (1992) 259-268. CrossRef