l0TV: A Sparse Optimization Method for Impulse Noise Image Restoration

Ganzhao Yuan, Bernard Ghanem

Research output: Contribution to journalArticlepeer-review

63 Scopus citations


Total Variation (TV) is an effective and popular prior model in the field of regularization-based image processing. This paper focuses on total variation for removing impulse noise in image restoration. This type of noise frequently arises in data acquisition and transmission due to many reasons, e.g. a faulty sensor or analog-to-digital converter errors. Removing this noise is an important task in image restoration. State-of-the-art methods such as Adaptive Outlier Pursuit(AOP), which is based on TV with l02-norm data fidelity, only give sub-optimal performance. In this paper, we propose a new sparse optimization method, called l0TV-PADMM, which solves the TV-based restoration problem with l0-norm data fidelity. To effectively deal with the resulting non-convex non-smooth optimization problem, we first reformulate it as an equivalent biconvex Mathematical Program with Equilibrium Constraints (MPEC), and then solve it using a proximal Alternating Direction Method of Multipliers (PADMM). Our l0TV-PADMM method finds a desirable solution to the original l0-norm optimization problem and is proven to be convergent under mild conditions. We apply l0TV-PADMM to the problems of image denoising and deblurring in the presence of impulse noise. Our extensive experiments demonstrate that l0TV-PADMM outperforms state-of-the-art image restoration methods.
Original languageEnglish (US)
Pages (from-to)352-364
Number of pages13
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number2
StatePublished - Dec 18 2017

Bibliographical note

KAUST Repository Item: Exported on 2020-04-23
Acknowledgements: We would like to thank Prof. Shaohua Pan for her helpful discussions on this paper. We also thank Prof. Ming Yan for sharing his code with us. This work was supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research and, in part, by the NSF-China (61772570, 61402182).

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computational Theory and Mathematics
  • Software
  • Applied Mathematics
  • Computer Vision and Pattern Recognition


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