Adaptive Variational Method for Restoring Color Images with High Density Impulse Noise

  • Authors:

  • Jun Liu;Haiyang Huang;Zhongdan Huan;Haili Zhang

  • Affiliations:

  • School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, P.R. China 100875;School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, P.R. China 100875;School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, P.R. China 100875;Department of Mathematics, University of Florida, Gainesville, USA 32611-8105

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 2010

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Abstract

In this paper, a new variational framework of restoring color images with impulse noise is presented. The novelty of this work is the introduction of an adaptively weighting data-fidelity term in the cost functional. The fidelity term is derived from statistical methods and contains two weighting functions as well as some statistical control parameters of noise. This method is based on the fact that impulse noise can be approximated as an additive noise with probability density function (PDF) being the finite mixture model. A Bayesian framework is then formulated in which likelihood functions are given by the mixture model. Inspired by the expectation-maximization (EM) algorithm, we present two models with variational framework in this study. The superiority of the proposed models is that: the weighting functions can effectively detect the noise in the image; with the noise information, the proposed algorithm can automatically balance the regularity of the restored image and the fidelity term by updating the weighting functions and the control parameters. These two steps ensure that one can obtain a good restoration even though the degraded color image is contaminated by impulse noise with large ration (90% or more). In addition, the numerical implementation of this algorithm is very fast by using a split algorithm. Some numerical experimental results and comparisons with other methods are provided to show the significant effectiveness of our approach.