TY - JOUR
T1 - Augmented Lagrangian Methods for $p$-Harmonic Flows with the Generalized Penalization Terms and Application to Image Processing
AU - Huibin Chang & Xue-Cheng Tai
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 - <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>