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A Fast Augmented Lagrangian Method for Euler’s Elastica Models

Published online by Cambridge University Press:  28 May 2015

Yuping Duan ,
Yu Wang  and
Jooyoung Hahn
Yuping Duan*
Affiliation:
Institute for Infocomm Research, Singapore
Yu Wang*
Affiliation:
Computer Science Department, Technion, Haifa 32000, Israel
Jooyoung Hahn*
Affiliation:
Institute for Mathematics and Scientific Computing, University of Graz, Austria
*
Corresponding author.Email address:duany@i2r.a-star.edu.sg
Corresponding author.Email address:yuwang@cs.technion.ac.il
Corresponding author.Email address:JooyoungHahn@gmail.com
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Abstract

In this paper, a fast algorithm for Euler’s elastica functional is proposed, in which the Euler’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.

Keywords

68U1065N2174S20Euler’s elasticaaugmented Lagrangian methodimage denoisingimage inpaintingimage zooming
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 1 , February 2013 , pp. 47 - 71
Copyright
Copyright © Global Science Press Limited 2013

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