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

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

Year:    2013

Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 1 : pp. 1–20

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2013.mssvm01

Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 1 : pp. 1–20

Published online:    2013-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    $p$-harmonic flows denoising generalized penalization terms saddle-point problem image processing augmented Lagrangian methods.