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Augmented Lagrangian Methods for p-Harmonic Flows with the Generalized Penalization Terms and Application to Image Processing

Published online by Cambridge University Press:  28 May 2015

Huibin Chang  and
Xue-Cheng Tai
Huibin Chang*
Affiliation:
School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387; Department of Mathematics, East China Normal University, Shanghai 200241, China
Xue-Cheng Tai*
Affiliation:
Department of Mathematics, University of Bergen, Johaness Brunsgate 12, Bergen 5007, Norway
*
Corresponding author.Email address:changhuibin@gmail.com
Corresponding author.Email address:xuechengtai@gmail.com
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Abstract

In this paper, we propose a generalized penalization technique and a convex constraint minimization approach for the p-harmonic flow problem following the ideas in [Kang & March, IEEE T. Image Process., 16 (2007), 2251-2261]. We use fast algorithms to solve the subproblems, such as the dual projection methods, primal-dual methods and augmented Lagrangian methods. With a special penalization term, some special algorithms are presented. Numerical experiments are given to demonstrate the performance of the proposed methods. We successfully show that our algorithms are effective and efficient due to two reasons: the solver for subproblem is fast in essence and there is no need to solve the subproblem accurately (even 2 inner iterations of the subproblem are enough). It is also observed that better PSNR values are produced using the new algorithms.

Keywords

68U1065N2174S20p-harmonic flowsdenoisinggeneralized penalization termssaddle-point problemimage processingaugmented Lagrangian methods
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 1 , February 2013 , pp. 1 - 20
Copyright
Copyright © Global Science Press Limited 2013

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