Exact optimization of discrete constrained total variation minimization problems

From LRDE

Revision as of 19:19, 5 January 2018 by Bot (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Abstract

This paper deals with the total variation minimization problem when the fidelity is either the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle L^2} -norm or the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle L^1} -norm. We propose an algorithm which computes the exact solution of these two problems after discretization. Our method relies on the decomposition of an image into its level sets. It maps the original problems into independent binary Markov Random Field optimization problems associated with each level set. Exact solutions of these binary problems are found thanks to minimum-cut techniques. We prove that these binary solutions are increasing and thus allow to reconstruct the solution of the original problems.


Bibtex (lrde.bib)

@TechReport{	  darbon.04.tr,
  author	= {J\'er\^ome Darbon and Marc Sigelle},
  title		= {Exact optimization of discrete constrained total variation
		  minimization problems},
  institution	= {ENST},
  year		= 2004,
  number	= {2004C004},
  address	= {Paris, France},
  month		= oct,
  annote	= {This technical report corresponds to the publication
		  darbon.04.iwcia. ; 200412-IWCIA},
  abstract	= {This paper deals with the total variation minimization
		  problem when the fidelity is either the $L^2$-norm or the
		  $L^1$-norm. We propose an algorithm which computes the
		  exact solution of these two problems after discretization.
		  Our method relies on the decomposition of an image into its
		  level sets. It maps the original problems into independent
		  binary Markov Random Field optimization problems associated
		  with each level set. Exact solutions of these binary
		  problems are found thanks to minimum-cut techniques. We
		  prove that these binary solutions are increasing and thus
		  allow to reconstruct the solution of the original
		  problems.}
}