Augmented Lagrangian Method for Generalized TV-Stokes Model

Authors:
Jooyoung Hahn;Chunlin Wu;Xue-Cheng Tai
Affiliations:
Institute of Mathematics and Scientific Computing, University of Graz, Graz, Austria;Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore;Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore and Mathematics Institute, University of Bergen, Bergen, Nor ...
Venue:
Journal of Scientific Computing
Year:
2012

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Abstract

In this paper, we propose a general form of TV-Stokes models and provide an efficient and fast numerical algorithm based on the augmented Lagrangian method. The proposed model and numerical algorithm can be used for a number of applications such as image inpainting, image decomposition, surface reconstruction from sparse gradient, direction denoising, and image denoising. Comparing with properties of different norms in regularity term and fidelity term, various results are investigated in applications. We numerically show that the proposed model recovers jump discontinuities of a data and discontinuities of the data gradient while reducing stair-case effect.