@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 = {<p style="text-align: justify;">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 &amp; 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 &nbsp;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 &nbsp;better PSNR values are produced using the new algorithms.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2013.mssvm01},
url = {https://global-sci.com/article/90620/augmented-lagrangian-methods-for-p-harmonic-flows-with-the-generalized-penalization-terms-and-application-to-image-processing}
}