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Recursive SURE for image recovery via total variation minimization

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Abstract

Recently, total variation regularization has become a standard technique, and even a basic tool for image denoising and deconvolution. Generally, the recovery quality strongly depends on the regularization parameter. In this work, we develop a recursive evaluation of Stein’s unbiased risk estimate (SURE) for the parameter selection, based on specific reconstruction algorithms. It enables us to monitor the evolution of mean squared error (MSE) during the iterations. In particular, to deal with large-scale data, we propose a Monte Carlo simulation for the practical computation of SURE, which is free of any explicit matrix operation. Experimental results show that the proposed recursive SURE could lead to highly accurate estimate of regularization parameter and nearly optimal restoration performance in terms of MSE.

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Notes

  1. See Sect. 4 for the complete comparisons between discrepancy principle and the proposed SURE.

  2. Note that the last constant term—\(\Vert \mathbf {x}_0\Vert _2^2/N\)—is irrelevant to the optimization of \(\widehat{\mathbf {x}}_\lambda \).

  3. We can see that the Chambolle’s iteration is readily incorporated into ADMM, see Sect. 2.1 for details.

  4. It is better to recognize the visual difference by zoom-in on larger screen.

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Authors and Affiliations

  1. National Key Laboratory of Science and Technology on Test Physics and Numerical Mathematics, Beijing, 100076, China

    Feng Xue, Jiaqi Liu & Xia Ai

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  1. Feng Xue
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  2. Jiaqi Liu
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  3. Xia Ai
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Correspondence to Feng Xue.

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This work was supported by the National Natural Science Foundation of China (No. 61401013).

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Xue, F., Liu, J. & Ai, X. Recursive SURE for image recovery via total variation minimization. SIViP 13, 795–803 (2019). https://doi.org/10.1007/s11760-019-01415-6

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