A fourth order dual method for staircase reduction in texture extraction and image restoration problems

Tony F. Chan, Selim Esedoglu, Frederick Park

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

57 Scopus citations

Abstract

We propose a novel fourth order dual method for the minimization of the non-smooth semi-norm ∥Δ∥1 when in amalgamation with a new staircase reducing texture decomposition model of image processing. The proposed model incorporating this high order energy is a variant of the Chambolle Lions denoising model that additionally utilizes a negative Sobolev norm. We claim that the dual method is faster and more stable than the current gradient descent time marching algorithms often used to minimize such energies. Moreover, a proof of convergence of the proposed method, in conjunction with the new model, will be provided. Lastly, we provide guidelines on how the new energy and proposed framework can be naturally incorporated into many popular texture extraction and restoration models of image processing.

Original languageEnglish (US)
Title of host publication2010 IEEE International Conference on Image Processing, ICIP 2010 - Proceedings
Pages4137-4140
Number of pages4
DOIs
StatePublished - Dec 1 2010
Externally publishedYes
Event2010 17th IEEE International Conference on Image Processing, ICIP 2010 - Hong Kong, Hong Kong
Duration: Sep 26 2010Sep 29 2010

Conference

Conference2010 17th IEEE International Conference on Image Processing, ICIP 2010
CountryHong Kong
CityHong Kong
Period09/26/1009/29/10

Keywords

  • Dual methods
  • Meyer norms
  • Staircase reduction
  • Texture removal
  • Total variation

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Signal Processing

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