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Table 1. Comparison of SNR obtained based on the true MSE and SUREImages Input SNR (dB) 4 8 12 16 20Boats TVD (11.02, 11.01) (13.12, 13.12) (15.62, 15.62) (18.38, 18.38) (21.43, 21.43)(512 × 512) RWD (11.90, 11.90) (14.06, 14.06) (16.49, 16.49) (19.09, 19.09) (21.92, 21.92)Barbara TVD (9.44, 9.44) (11.66, 11.66) (14.48, 14.48) (17.71, 17.71) (21.16, 21.16)(512 × 512) RWD (10.55, 10.55) (12.87, 12.87) (15.58, 15.58) (18.61, 18.61) (21.89, 21.89)Peppers TVD (11.18, 11.18) (13.70, 13.70) (16.36, 16.36) (19.18, 19.18) (22.18, 22.18)(256 × 256) RWD (12.03, 12.03) (14.59, 14.59) (17.26, 17.26) (20.04, 20.04) (22.88, 22.88)Shepp-Logan TVD (15.21, 15.21) (18.84, 18.82) (22.71, 22.71) (26.30, 26.30) (30.14, 30.12)(256 × 256) RWD (13.92, 13.92) (17.51, 17.51) (21.33, 21.33) (24.96, 24.96) (28.82, 28.82)MSE320300280260240220200180160TRUE MSESURE17.4 20.4 23.5 26.7 29.8 32.9 36 39.1 42.2 45.4λFig. 3. True MSE and SURE as a function of λ for TVD.MSE240220200180160140TRUE MSESURE45.5 63.8 82.3 100.8 119.2 137.7 156.2 174.6 193.1 211.5λFig. 4. True MSE and SURE as a function of λ for RWD.output of the denoising algorithm and does not require anyknowledge of its internal working. We did illustrate and validatethe method by optimization of the parameters of somepopular denoising algorithms. We found that SURE computedusing our method perfectly predicts the true MSE inall the cases tested. Moreover, the SNR obtained by SUREbasedoptimization is in almost perfect agreement with theoracle solution (minimum MSE). This suggests that Monte-Carlo SURE can be reliably employed for data-driven adjustmentof parameters in a large variety of denoising problemsprovided that the data is corrupted by Gaussian noise.6. REFERENCES[1] R. Molina, A. K. Katsaggelos, and J. Mateos, “Bayesianand regularization methods for hyperparameter estimationin image restoration,” IEEE Trans. Image Process.,vol. 8, no. 2, pp. 231–246, 1999.[2] N. P. Galatsanos and A. K. Katsaggelos, “Methodsfor choosing the regularization parameter and estimatingthe noise variance in image restoration and their relation,”IEEE Trans. Image Process., vol. 1, no. 3, pp.322–336, 1992.[3] W. C. Karl, “Regularization in image restoration andreconstruction,” in Handbook of Image & Video Processing,A. Bovik, Ed., pp. 183–202. ELSEVIER, 2ndedition, 2005.[4] G. Gilboa, N. Sochen, and Y. Y. Zeevi, “Estimation ofoptimal PDE-based denoising in the SNR sense,” IEEETrans. Image Process., vol. 15, no. 8, pp. 2269–2280,2006.[5] C. Stein, “Estimation of the mean of a multivariate normaldistribution,” Ann. Statist., vol. 9, pp. 1135–1151,1981.[6] D. L. Donoho and I. M. Johnstone, “Adapting to unknownsmoothness via wavelet shrinkage,” J. Amer.Statist. Assoc., vol. 90, no. 432, pp. 1200–1224, 1995.[7] X. -P. Zhang and M. D. Desai, “Adaptive denoisingbasedonSURErisk,” IEEE Signal Process. Lett., vol.5, no. 10, pp. 265–267, 1998.[8] F. Luisier, T. Blu, and M. Unser, “A new SUREapproach to image denoising: Interscale orthonormalwavelet thresholding,” IEEE Trans. Image Process.,vol.16, no. 3, pp. 593–606, 2007.[9] M. A. T. Figueiredo, J. B. Dias, J. P. Oliveira, andR. D. Nowak, “On total variation denoising: A newMajorization-Minimization algorithm and an experimentalcomparison with wavalet denoising,” Proceedingsof IEEE International Conference on Image Processing(ICIP 2006), Atlanta, GA, USA, pp. 2633–2636,October 2006.908