ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - January 2000 - Volume 5

Research Article

Image deblurring, spectrum interpolation and application to satellite imaging

Durand, Sylvaina1a2, Malgouyres, Françoisa1 and Rougé, Bernarda3

a1 CMLA, ENS Cachan, 61 avenue du président Wilson, 94235 Cachan Cedex, France; sdurand@cmla.ens-cachan.fr. & malgouy@cmla.ens-cachan.fr.

a2 LAMFA, Université de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens Cedex 1, France.

a3 CNES, DGAT/SH/QTIS, 18 avenue E. Belin, 31401 Toulouse Cedex 4, France; rouge@cnes.fr.

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.

(Received February 14 2000)

(Online publication August 15 2002)

Key Words:

  • Image restoration;
  • deblurring;
  • wavelet-packets;
  • Total Variation;
  • spectrum interpolation.

Mathematics Subject Classification:

  • 68U10
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