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2014, 4(3): 209-225. doi: 10.3934/naco.2014.4.209

Two-step methods for image zooming using duality strategies

 1 College of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China 2 Department of Information and Computing Science, Changsha University, Changsha, 410003, China 3 College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China

Received  November 2013 Revised  July 2014 Published  September 2014

In this paper we propose two two-step methods for image zooming using duality strategies. In the first method, instead of smoothing the normal vector directly as did in the first step of the classical LOT model, we reconstruct the unit normal vector by means of Chambolle's dual formulation. Then, we adopt the split Bregman iteration to obtain the zoomed image in the second step. The second method is based on the TV-Stokes model. By smoothing the tangential vector and imposing the divergence free condition, we propose an image zooming method based on the TV-Stokes model using the dual formulation. Furthermore, we give the convergence analysis of the proposed algorithms. Numerical experiments show the efficiency of the proposed methods.
Citation: Tingting Wu, Yufei Yang, Huichao Jing. Two-step methods for image zooming using duality strategies. Numerical Algebra, Control & Optimization, 2014, 4 (3) : 209-225. doi: 10.3934/naco.2014.4.209
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References:
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