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Journal of Mathematical Imaging and Vision

, Volume 26, Issue 1–2, pp 167–184 | Cite as

Iterative Total Variation Regularization with Non-Quadratic Fidelity

  • Lin HeEmail author
  • Martin Burger
  • Stanley J. Osher
Article

Abstract

A generalized iterative regularization procedure based on the total variation penalization is introduced for image denoising models with non-quadratic convex fidelity terms. By using a suitable sequence of penalty parameters we solve the issue of solvability of minimization problems arising in each step of the iterative procedure, which has been encountered in a recently developed iterative total variation procedure Furthermore, we obtain rigorous convergence results for exact and noisy data.

We test the behaviour of the algorithm on real images in several numerical experiments using L 1 and L 2 fitting terms. Moreover, we compare the results with other state-of-the art multiscale techniques for total variation based image restoration.

Keywords

iterative regularization total variation methods image denoising multiscale methods Bregman distances 

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Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.UCLA Mathematics DepartmentLos AngelesUSA
  2. 2.Institut für Industriemathematik, Johannes Kepler UniversitätLinzAustria

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