A Fast Augmented Lagrangian Method for Euler%26apos;s Elastica Models

作者：Duan Yuping^*; Wang Yu; Hahn Jooyoung

来源：Numerical Mathematics: Theory, Methods and Applications , 2013, 6(1): 47-71.

DOI：10.4208/nmtma.2013.mssvm03

• Euler%26apos
• s elastica
• augmented Lagrangian method
• image denoising
• image inpainting
• image zooming

In this paper, a fast algorithm for Euler%26apos;s elastica functional is proposed, in which the Euler%26apos;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.

• 出版日期2013-2