Image restoration with discrete constrained Total Variation—Part~II: Levelable functions, convex priors and non-convex case

From LRDE

Abstract

In Part II of this paper we extend the results obtained in Part I for total variation minimization in image restoration towards the following directions: first we investigate the decomposability property of energies on levels, which leads us to introduce the concept of levelable regularization functions (which TV is the paradigm of). We show that convex levelable posterior energies can be minimized exactly using the level-independant cut optimization scheme seen in part I. Next we extend this graph cut scheme optimization scheme to the case of non-convex levelable energies. We present convincing restoration results for images corrupted with impulsive noise. We also provide a minimum-cost based algorithm which computes a global minimizer for Markov Random Field with convex priors. Last we show that non-levelable models with convex local conditional posterior energies such as the class of generalized gaussian models can be exactly minimized with a generalized coupled Simulated Annealing.


Bibtex (lrde.bib)

@Article{	  darbon.06.jmivb,
  author	= {J\'er\^ome Darbon and Marc Sigelle},
  title		= {Image restoration with discrete constrained {T}otal
		  {Variation}---Part~{II}: Levelable functions, convex priors
		  and non-convex case},
  journal	= {Journal of Mathematical Imaging and Vision},
  year		= 2006,
  volume	= 26,
  number	= 3,
  month		= dec,
  pages		= {277--291},
  abstract	= {In Part II of this paper we extend the results obtained in
		  Part I for total variation minimization in image
		  restoration towards the following directions: first we
		  investigate the decomposability property of energies on
		  levels, which leads us to introduce the concept of
		  levelable regularization functions (which TV is the
		  paradigm of). We show that convex levelable posterior
		  energies can be minimized exactly using the
		  level-independant cut optimization scheme seen in part I.
		  Next we extend this graph cut scheme optimization scheme to
		  the case of non-convex levelable energies. We present
		  convincing restoration results for images corrupted with
		  impulsive noise. We also provide a minimum-cost based
		  algorithm which computes a global minimizer for Markov
		  Random Field with convex priors. Last we show that
		  non-levelable models with convex local conditional
		  posterior energies such as the class of generalized
		  gaussian models can be exactly minimized with a generalized
		  coupled Simulated Annealing.}
}