Nonlocal Variational Image Deblurring Models in the Presence of Gaussian or Impulse Noise

Authors:
Miyoun Jung;Luminita A. Vese
Affiliations:
Department of Mathematics, University of California, Los Angeles, Los Angeles, USA CA 90095-1555;Department of Mathematics, University of California, Los Angeles, Los Angeles, USA CA 90095-1555
Venue:
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Year:
2009

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Abstract

We wish to recover an image corrupted by blur and Gaussian or impulse noise, in a variational framework. We use two data-fidelity terms depending on the noise, and several local and nonlocal regularizers. Inspired by Buades-Coll-Morel, Gilboa-Osher, and other nonlocal models, we propose nonlocal versions of the Ambrosio-Tortorelli and Shah approximations to Mumford-Shah-like regularizing functionals, with applications to image deblurring in the presence of noise. In the case of impulse noise model, we propose a necessary preprocessing step for the computation of the weight function. Experimental results show that these nonlocal MS regularizers yield better results than the corresponding local ones (proposed for deblurring by Bar et al.) in both noise models; moreover, these perform better than the nonlocal total variation in the presence of impulse noise. Characterization of minimizers is also given.