Total Variation Restoration of Images Corrupted by Poisson Noise with Iterated Conditional Expectations

  • Rémy Abergel
  • Cécile Louchet
  • Lionel Moisan
  • Tieyong Zeng
Conference paper

DOI: 10.1007/978-3-319-18461-6_15

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9087)
Cite this paper as:
Abergel R., Louchet C., Moisan L., Zeng T. (2015) Total Variation Restoration of Images Corrupted by Poisson Noise with Iterated Conditional Expectations. In: Aujol JF., Nikolova M., Papadakis N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2015. Lecture Notes in Computer Science, vol 9087. Springer, Cham

Abstract

Interpreting the celebrated Rudin-Osher-Fatemi (ROF) model in a Bayesian framework has led to interesting new variants for Total Variation image denoising in the last decade. The Posterior Mean variant avoids the so-called staircasing artifact of the ROF model but is computationally very expensive. Another recent variant, called TV-ICE (for Iterated Conditional Expectation), delivers very similar images but uses a much faster fixed-point algorithm. In the present work, we consider the TV-ICE approach in the case of a Poisson noise model. We derive an explicit form of the recursion operator, and show linear convergence of the algorithm, as well as the absence of staircasing effect. We also provide a numerical algorithm that carefully handles precision and numerical overflow issues, and show experiments that illustrate the interest of this Poisson TV-ICE variant.

Keywords

Poisson noise removal Image denoising Total variation Posterior mean Marginal conditional mean Staircasing effect Fixed-point algorithm Incomplete gamma function 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Rémy Abergel
    • 1
  • Cécile Louchet
    • 2
  • Lionel Moisan
    • 1
  • Tieyong Zeng
    • 3
  1. 1.MAP5 (CNRS UMR 8145)Université Paris DescartesParisFrance
  2. 2.MAPMO (CNRS UMR 6628)Université d’OrléansParisFrance
  3. 3.Department of MathematicsHong Kong Baptist UniversityKowloon TongHong Kong

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