Image deblurring, spectrum interpolation and application to satellite imaging
ESAIM: Control, Optimisation and Calculus of Variations, Tome 5 (2000), pp. 445-475.
@article{COCV_2000__5__445_0,
     author = {Durand, Sylvain and Malgouyres, Fran\c{c}ois and Roug\'e, Bernard},
     title = {Image deblurring, spectrum interpolation and application to satellite imaging},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {445--475},
     publisher = {EDP-Sciences},
     volume = {5},
     year = {2000},
     mrnumber = {1789371},
     zbl = {0946.68150},
     language = {en},
     url = {http://archive.numdam.org/item/COCV_2000__5__445_0/}
}
TY  - JOUR
AU  - Durand, Sylvain
AU  - Malgouyres, François
AU  - Rougé, Bernard
TI  - Image deblurring, spectrum interpolation and application to satellite imaging
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2000
SP  - 445
EP  - 475
VL  - 5
PB  - EDP-Sciences
UR  - http://archive.numdam.org/item/COCV_2000__5__445_0/
LA  - en
ID  - COCV_2000__5__445_0
ER  - 
%0 Journal Article
%A Durand, Sylvain
%A Malgouyres, François
%A Rougé, Bernard
%T Image deblurring, spectrum interpolation and application to satellite imaging
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2000
%P 445-475
%V 5
%I EDP-Sciences
%U http://archive.numdam.org/item/COCV_2000__5__445_0/
%G en
%F COCV_2000__5__445_0
Durand, Sylvain; Malgouyres, François; Rougé, Bernard. Image deblurring, spectrum interpolation and application to satellite imaging. ESAIM: Control, Optimisation and Calculus of Variations, Tome 5 (2000), pp. 445-475. http://archive.numdam.org/item/COCV_2000__5__445_0/

[1] R. Acart and C. Vogel, Analysis of bounded variation methods for ill-posed problems. Inverse Problems 10 ( 1994) 1217-1229. | MR | Zbl

[2] H.C. Andrews and B.R. Hunt, Digital signal processing. Tech. Englewood Cliffs, NJ: Prentice-Hall ( 1977).

[3] S.M. Berman, Sojournes and Extremes os Stochastic Processes. Wadsworth, Reading, MA ( 1989). | Zbl

[4] A. Cohen, R. De Vore, P. Petrushev and H. Xu, Nonlinear Approximation and the Space BV (ℝ 2) (preprint). | Zbl

[5] V. Caselles, J.L. Lisani, J.M. Morel and G. Sapiro, Shape Preserving Local Histogram Modification. IEEE Trans. Image Process. 8 ( 1999).

[6] 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. | MR | Zbl

[7] 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).

[8] A. Chambolle and P.L. Lions, Image recovery via Total Variation minimisation and related problems. Numer. Math. 76 ( 1997) 167-188. IEEE Trans. Image Process. | MR | Zbl

[9] 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).

[10] R.R. Coifman and D.L. Donoho, Translation-invariant de-noising. Technical Report 475, Standford University ( 1995). | Zbl

[11] 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. | MR | Zbl

[12] G. Demoment, Image reconstruction and restoration: Overview of Common Estimation Structures and Problems. IEEE Trans. Acoust. Speech Signal Process. 37 ( 1989).

[13] D. Donoho and I.M. Johnstone, Minimax Estimation via wavelet shrinkage. Tech. Report, Dept. of Stat., Stanford Univ. ( 1992).

[14] D.L. Donoho and I.M. Johnstone, Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 ( 1994) 425-455. | MR | Zbl

[15] L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions. Studies in advanced mathematics, CRS Press Inc. ( 1992). | MR | Zbl

[16] F. Guichard and F. Malgouyres, Total Variation Based interpolation, in Proc. of European Signal Processing Conference (EUSIPCO-98), Vol. 3 ( 1998) 1741-1744.

[17] I.M. Johnstone and B.W. Silverman, Wavelet threshold estimators for data with correlated noise. Technical report, Standford University ( 1994).

[18] T. Kailath, A View of Three Decades of Linear Filtering Theory. IEEE Trans. Inform. Theory IT20 ( 1974). | MR | Zbl

[19] J. Kalifa, Restauration minimax et déconvolution dans un base d'ondelettes miroirs. Thèse, École Polytechnique ( 1999).

[20] J. Kalifa, S. Mallat and B. Rougé, Restauration d'images par paquets d'ondelettes. 16e Colloque GRETSI ( 1997).

[21] J. Kalifa, S. Mallat and B. Rougé, Image Deconvolution in Mirror Wavelet Bases. IEEE, ICIP'98.

[22] 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). | MR | Zbl

[23] M. Lindenbaum, M. Fischer and A. Bruckstein, On Gabor's contribution to image enhancement. PR. 27 ( 1994) 1-8.

[24] S. Mallat, A theory for multiresolution signal decomposition: The wavelet representation. IEEE Trans. Patern Analysis and Machine Intelligence II ( 1989). | Zbl

[25] S. Mallat, A Wavelet Tour of Signal Processing. Academic Press ( 1998). | MR | Zbl

[26] Y. Meyer, Ondelettes et opérateurs, Hermann ( 1990) Tome 1. | Zbl

[27] Y. Meyer, Les ondelettes, algorithmes et applications. Armand Colin ( 1992).

[28] M. Nikolova, Local strong homogeneity of a regularized estimator. SIAM (to appear). | MR | Zbl

[29] B. Rougé, Remarks about space-frequency and space-scaleto 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). | Zbl

[30] B. Rougé, Fixed Chosen Noise Restauration (FCNR). IEEE 95 Philadelphia (U.S.A.).

[31] L. Rudin, S. Osher and E. Fatemi, Nonlinear Total Variation based noise removal algorithms. Physica D 60 ( 1992259-268. | MR | Zbl