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What is the problem?

Observed satellite images are corrupted in the following way :

 Notations :
X0 = original image

Y = observed image

H = convolution operator (symmetric kernel)

N additive white Gaussian noise

Example : image extracted from Nîmes,
SPOT 5 simulation- (C) CNES
Original image
Corrupted image
We must reconstruct the image, avoiding noise amplification. 
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André Jalobeanu - 24 Aug 1998