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  • Research Article
  • Open Access

Restoration of Astrophysical Images—The Case of Poisson Data with Additive Gaussian Noise

EURASIP Journal on Advances in Signal Processing20052005:643143

https://doi.org/10.1155/ASP.2005.2500

Received: 28 May 2004

Published: 14 September 2005

Abstract

We consider the problem of restoring astronomical images acquired with charge coupled device cameras. The astronomical object is first blurred by the point spread function of the instrument-atmosphere set. The resulting convolved image is corrupted by a Poissonian noise due to low light intensity, then, a Gaussian white noise is added during the electronic read-out operation. We show first that the split gradient method (SGM) previously proposed can be used to obtain maximum likelihood (ML) iterative algorithms adapted in such noise combinations. However, when ML algorithms are used for image restoration, whatever the noise process is, instabilities due to noise amplification appear when the iteration number increases. To avoid this drawback and to obtain physically meaningful solutions, we introduce various classical penalization-regularization terms to impose a smoothness property on the solution. We show that the SGM can be extended to such penalized ML objective functions, allowing us to obtain new algorithms leading to maximum a posteriori stable solutions. The proposed algorithms are checked on typical astronomical images and the choice of the penalty function is discussed following the kind of object.

Keywords and phrases

  • restoration
  • astronomic images
  • Poisson transformation
  • MAP estimation
  • regularization
  • iterative algorithms

Authors’ Affiliations

(1)
Laboratoire d'Astrophysique, Université de Nice Sophia Antipolis, CNRS UMR6525, Nice Cedex 2, France

Copyright

© Lantéri and Theys 2005

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