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Multiplicative Denoising Based on Linearized Alternating Direction Method Using Discrepancy Function Constraint

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Abstract

The multiplicative noise (speckle) in coherent imaging systems such as synthetic aperture radar makes it difficult to interpret observed images. Recently, the total variation (TV) models have received much interest in removing the speckle due to the strong edge preserving ability and low computational cost of the TV regularizer. However, the classical methods have difficulties in two aspects: one is how to efficiently compute the solution of the models with special data-fidelity terms, the other is how to choose the regularization parameter since the variational models are rather sensitive to the parameter. In this paper, we propose a new linearized alternating direction method, which is able to handle the data-fidelity term efficiently, and meanwhile estimate the optimal value of the regularization parameter exactly based on a discrepancy function constraint. We further establish the global convergence of the proposed algorithm. Numerical experiments demonstrate that our methods overall outperform the current state-of-the-art methods for multiplicative noise removal.

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Acknowledgments

We are appreciative of the anonymous reviewers’constructive comments, with which great improvements have been made in this manuscript. The work was supported in part by the National Natural Science Foundation of China under Grant 61271014.

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Authors and Affiliations

  1. Department of Mathematics, School of Biomedical Engineering, Third Military Medical University, Chongqing, 400038, Chongqing, People’s Republic of China

    Dai-Qiang Chen

  2. School of Automation, Chongqing University, Changsha , 401331, Chongqing, People’s Republic of China

    Yan Zhou

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  1. Dai-Qiang Chen
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  2. Yan Zhou
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Correspondence to Dai-Qiang Chen.

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Chen, DQ., Zhou, Y. Multiplicative Denoising Based on Linearized Alternating Direction Method Using Discrepancy Function Constraint. J Sci Comput 60, 483–504 (2014). https://doi.org/10.1007/s10915-013-9803-z

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  • DOI: https://doi.org/10.1007/s10915-013-9803-z

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