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On Nonmonotone Chambolle Gradient Projection Algorithms for Total Variation Image Restoration

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Abstract

The main aim of this paper is to accelerate the Chambolle gradient projection method for total variation image restoration. In the proposed minimization method model, we use the well known Barzilai-Borwein stepsize instead of the constant time stepsize in Chambolle’s method. Further, we adopt the adaptive nonmonotone line search scheme proposed by Dai and Fletcher to guarantee the global convergence of the proposed method. Numerical results illustrate the efficiency of this method and indicate that such a nonmonotone method is more suitable to solve some large-scale inverse problems.

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Correspondence to Gaohang Yu.

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This work was partly supported by the Research Grant Council of Hong Kong, a postdoctoral fellowship from the Department of Applied Mathematics at the Hong Kong Polytechnic University (1-ZV0K), a grant from the Ph.D. Programs Foundation of Ministry of Education of China (No.200805581022) and the National Natural Science Foundation of China (No.10571171, 10831006 and 60804008), and the CAS grant kjcx-yw-s7-03.

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Yu, G., Qi, L. & Dai, Y. On Nonmonotone Chambolle Gradient Projection Algorithms for Total Variation Image Restoration. J Math Imaging Vis 35, 143–154 (2009). https://doi.org/10.1007/s10851-009-0160-3

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