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On the convergence of recursive SURE for total variation minimization

  • Feng Xue EMAIL logo , Xia Ai and Jiaqi Liu
Published/Copyright: January 9, 2021

Abstract

Recently, total variation (TV) regularization has become a standard technique for image recovery. The mean squared error (MSE) of the reconstruction can be reliably estimated by Stein’s unbiased risk estimate (SURE). In this work, we develop two recursive evaluations of SURE, based on Chambolle’s projection method (CPM) for TV denoising and alternating direction method of multipliers (ADMM) for TV deconvolution, respectively. In particular, from the proximal point perspective, we provide the convergence analysis for both iterative schemes and the corresponding Jacobian recursions, in terms of the solution distance, from which follows the convergence of noise evolution of Monte-Carlo simulation in practical computations. The theoretical analysis is supported by numerical examples.

MSC 2010: 68U10; 94A08

Award Identifier / Grant number: 62071028

Funding statement: This work was supported by the National Natural Science Foundation of China under Grant No. 62071028.

Acknowledgements

The authors would like to thank the anonymous reviewers for the helpful comments, which substantially improved the theoretical quality of this paper.

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Received: 2018-02-13
Revised: 2020-07-24
Accepted: 2020-11-17
Published Online: 2021-01-09
Published in Print: 2021-04-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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