@Article{NMTMA-6-47,
author = {Yuping Duan, Yu Wang and Jooyoung Hahn},
title = {A Fast Augmented Lagrangian Method for Euler's Elastica Models},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2013},
volume = {6},
number = {1},
pages = {47--71},
abstract = {<p style="text-align: justify;">In this paper, a fast algorithm for Euler&#39;s elastica functional is proposed,
in which the Euler&#39;s elastica functional is reformulated as a constrained
minimization problem. Combining the augmented Lagrangian method and operator
splitting techniques, the resulting saddle-point problem is solved by a serial
of subproblems. To tackle the nonlinear constraints arising in the model, a novel
fixed-point-based approach is proposed so that all the subproblems either is a
linear problem or has a closed-form solution. We show the good performance of our
approach in terms of speed and reliability using numerous numerical examples on
synthetic, real-world and medical images for image denoising, image inpainting
and image zooming problems.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2013.mssvm03},
url = {http://global-sci.org/intro/article_detail/nmtma/5894.html}
}