TY - JOUR
T1 - A Fast Augmented Lagrangian Method for Euler's Elastica Models
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 47
EP - 71
PY - 2013
DA - 2013/06
SN - 6
DO - http://doi.org/10.4208/nmtma.2013.mssvm03
UR - https://global-sci.org/intro/article_detail/nmtma/5894.html
KW - Euler's elastica, augmented Lagrangian method, image denoising, image inpainting,
image zooming.
AB - <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>