Minimization of an Edge-Preserving Regularization Functional by Conjugate Gradient Type Methods

Jian-Feng CAI, Raymond CHAN, Benedetta MORINI

Research output: Book Chapters | Papers in Conference ProceedingsConference paper (refereed)Researchpeer-review


Recently, a powerful two-phase method for removing impulse noise has been developed. It gives a satisfactory result even for images with 90% pixels corrupted by impulse noise. However, the two-phase method is not computationally efficient, because it requires the minimization of a non-smooth functional in the second phase, which is done by a relaxation-based method. In this paper, we remove the non-smooth term from the functional, and call for the minimization of a smooth one. The minimizer is then found by using a conjugate gradient method proposed by J. Sun and J. Zhang. We prove the global convergence of the conjugate gradient type method applied to our functional. Simulation results show that our method is several times faster than the relaxation-based method when the noise ratio is high.
Original languageEnglish
Title of host publicationImage Processing Based on Partial Differential Equations: Proceedings of the International Conference on PDE-Based Image Processing and Related Inverse Problems, CMA, Oslo, August 8-12, 2005
EditorsXue-Cheng TAI, Knut-Andreas LIE, Tony F. CHAN, Stanley OSHER
PublisherSpringer Berlin Heidelberg
Number of pages14
ISBN (Electronic)9783540332671
ISBN (Print)9783540332664, 9783642069901
Publication statusPublished - 2007
Externally publishedYes

Publication series

NameMathematics and Visualization
PublisherSpringer Berlin, Heidelberg
ISSN (Print)1612-3786
ISSN (Electronic)2197-666X


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