Total generalized variation restoration with non-quadratic fidelity View Full Text


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Article Info

DATE

2017-07-19

AUTHORS

Yiming Gao, Fang Liu, Xiaoping Yang

ABSTRACT

Total variation (TV) based Models have been widely used in image restoration problems. However, these models are always accompanied by staircase effect due to the property of bounded variation (BV) space. In this paper, we present two high order variational models based on total generalized variation (TGV) with two common and important non-quadratic fidelity data terms for blurred images corrupted by impulsive and Poisson noises. Since the direct extension of alternative direction method of multipliers (ADMM) to solve three-block convex minimization problems is not necessarily convergent, we develop an efficient algorithm called Prediction–Correction ADMM to solve our models and also show the convergence of the proposed method. Moreover, we extend our models to deal with color images restoration. Numerical experiments demonstrate that the proposed high order models can reduce staircase effect while preserving edges and outperform classical TV based models in SNR and SSIM values. More... »

PAGES

1459-1484

References to SciGraph publications

  • 2015-02-07. Preconditioned Douglas–Rachford Algorithms for TV- and TGV-Regularized Variational Imaging Problems in JOURNAL OF MATHEMATICAL IMAGING AND VISION
  • 2009. Bregman-EM-TV Methods with Application to Optical Nanoscopy in SCALE SPACE AND VARIATIONAL METHODS IN COMPUTER VISION
  • 2009-12-05. Removing Multiplicative Noise by Douglas-Rachford Splitting Methods in JOURNAL OF MATHEMATICAL IMAGING AND VISION
  • 2014-04-02. Recovering Piecewise Smooth Multichannel Images by Minimization of Convex Functionals with Total Generalized Variation Penalty in EFFICIENT ALGORITHMS FOR GLOBAL OPTIMIZATION METHODS IN COMPUTER VISION
  • 2009. Split Bregman Algorithm, Douglas-Rachford Splitting and Frame Shrinkage in SCALE SPACE AND VARIATIONAL METHODS IN COMPUTER VISION
  • 2004-01. Regularizing Flows for Constrained Matrix-Valued Images in JOURNAL OF MATHEMATICAL IMAGING AND VISION
  • 2007-11-06. Parallel splitting augmented Lagrangian methods for monotone structured variational inequalities in COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
  • 2000-08. Alternating Direction Method with Self-Adaptive Penalty Parameters for Monotone Variational Inequalities in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2010-12-21. A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging in JOURNAL OF MATHEMATICAL IMAGING AND VISION
  • 2014-10-17. The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent in MATHEMATICAL PROGRAMMING
  • 2007-03-30. A Variational Approach to Reconstructing Images Corrupted by Poisson Noise in JOURNAL OF MATHEMATICAL IMAGING AND VISION
  • 2011-03-17. Augmented Lagrangian Method for Total Variation Based Image Restoration and Segmentation Over Triangulated Surfaces in JOURNAL OF SCIENTIFIC COMPUTING
  • 1992-04. On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators in MATHEMATICAL PROGRAMMING
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    http://scigraph.springernature.com/pub.10.1007/s11045-017-0512-x

    DOI

    http://dx.doi.org/10.1007/s11045-017-0512-x

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