Two-step methods for image zooming using duality strategies

Tingting Wu; Yufei Yang; Huichao Jing

doi:10.3934/naco.2014.4.209

Article Contents

2014, Volume 4, Issue 3: 209-225. Doi: 10.3934/naco.2014.4.209

This issue Previous Article Convergence analysis of the weighted state space search algorithm for recurrent neural networks Next Article Sparse inverse incidence matrices for Schilders' factorization applied to resistor network modeling

Two-step methods for image zooming using duality strategies

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

Received: November 2013

Revised: July 2014

Published: August 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 65K10, 65C20; Secondary: 94A08.

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