Volume 6, Issue 1
Augmented Lagrangian Methods for $p$-Harmonic Flows with the Generalized Penalization Terms and Application to Image Processing

Huibin Chang & Xue-Cheng Tai

Numer. Math. Theor. Meth. Appl., 6 (2013), pp. 1-20.

Published online: 2013-06

Preview Full PDF 566 3777
Export citation
  • 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

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

  • AMS Subject Headings

68U10, 65N21, 74S20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{NMTMA-6-1, author = {}, title = {Augmented Lagrangian Methods for $p$-Harmonic Flows with the Generalized Penalization Terms and Application to Image Processing}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2013}, volume = {6}, number = {1}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2013.mssvm01}, url = {http://global-sci.org/intro/article_detail/nmtma/5892.html} }
TY - JOUR T1 - Augmented Lagrangian Methods for $p$-Harmonic Flows with the Generalized Penalization Terms and Application to Image Processing JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 1 EP - 20 PY - 2013 DA - 2013/06 SN - 6 DO - http://doi.org/10.4208/nmtma.2013.mssvm01 UR - https://global-sci.org/intro/article_detail/nmtma/5892.html KW - $p$-harmonic flows, denoising, generalized penalization terms, saddle-point problem, image processing, augmented Lagrangian methods. AB -

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.

Huibin Chang & Xue-Cheng Tai. (2020). Augmented Lagrangian Methods for $p$-Harmonic Flows with the Generalized Penalization Terms and Application to Image Processing. Numerical Mathematics: Theory, Methods and Applications. 6 (1). 1-20. doi:10.4208/nmtma.2013.mssvm01
Copy to clipboard
The citation has been copied to your clipboard