2000 character limit reached
Whiteness-based bilevel learning of regularization parameters in imaging (2403.07026v1)
Published 10 Mar 2024 in math.OC, cs.LG, and eess.IV
Abstract: We consider an unsupervised bilevel optimization strategy for learning regularization parameters in the context of imaging inverse problems in the presence of additive white Gaussian noise. Compared to supervised and semi-supervised metrics relying either on the prior knowledge of reference data and/or on some (partial) knowledge on the noise statistics, the proposed approach optimizes the whiteness of the residual between the observed data and the observation model with no need of ground-truth data.We validate the approach on standard Total Variation-regularized image deconvolution problems which show that the proposed quality metric provides estimates close to the mean-square error oracle and to discrepancy-based principles.
- E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory, vol. 52, no. 2, 2006.
- L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D: Nonlinear Phen., vol. 60, no. 1, 1992.
- L. Calatroni, A. Lanza, M. Pragliola, and F. Sgallari, “Adaptive parameter selection for weighted-TV image reconstruction problems,” Journal of Physics: Conference Series, vol. 1476, no. 1, p. 012003, 2020.
- M. Pragliola, L. Calatroni, A. Lanza, and F. Sgallari, “On and beyond total variation regularization in imaging: The role of space variance,” SIAM Rev., vol. 65, no. 3, pp. 601–685, 2023.
- P. C. Hansen, “Analysis of discrete ill-posed problems by means of the L-curve,” SIAM Rev., vol. 34, no. 4, pp. 561–580, 1992.
- V. A. Morozov, “On the solution of functional equations by the method of regularization,” Doklady Mathematics, vol. 7, pp. 414–417, 1966.
- J. Pesquet, A. Benazza-Benyahia, and C. Chaux, “A SURE approach for digital signal/image deconvolution problems,” IEEE Trans. Signal Process., vol. 57, no. 12, 2009.
- E. Haber and L. Tenorio, “Learning regularization functionals: a supervised training approach,” Inverse Probl., vol. 19, no. 3, pp. 611–626, 2003.
- K. G. G. Samuel and M. F. Tappen, “Learning optimized MAP estimates in continuously-valued MRF models,” in 2009 CVPR, 2009.
- F. Pedregosa, “Hyperparameter optimization with approximate gradient,” in ICML, vol. 48. New York, USA: PMLR, 2016, pp. 737–746.
- K. Kunisch and T. Pock, “A bilevel optimization approach for parameter learning in variational models,” SIAM J. on Imaging Sci., vol. 6, no. 2, 2013.
- J. C. De los Reyes, C.-B. Schönlieb, and T. Valkonen, “Bilevel parameter learning for higher-order total variation regularisation models,” J. of Math. Imaging Vis., vol. 57, no. 1, 2017.
- C. Crockett and J. A. Fessler, “Bilevel methods for image reconstruction,” Found. Trends Signal Process., vol. 15, no. 2-3, 2022.
- J. Fehrenbach, M. Nikolova, G. Steidl, and P. Weiss, “Bilevel image denoising using gaussianity tests,” in SSVM. Cham: Springer International Publishing, 2015, pp. 117–128.
- A. Lanza, M. Pragliola, and F. Sgallari, “Residual whiteness principle for parameter-free image restoration,” Electron. Trans. Numer. Anal., vol. 53, pp. 329–351, 2020.
- M. Pragliola, L. Calatroni, A. Lanza, and F. Sgallari, “ADMM-based residual whiteness principle for automatic parameter selection in single image super-resolution problems,” J. Math. Imaging Vis., vol. 65, no. 1, pp. 99–123, 2023.
- F. Bevilacqua, A. Lanza, M. Pragliola, and F. Sgallari, “Whiteness-based parameter selection for Poisson data in variational image processing,” Appl. Math. Model., vol. 117, pp. 197–218, 2023.
- A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vis., vol. 20, no. 1, pp. 89–97, 2004.
- D. R. Martin, C. C. Fowlkes, D. Tal, and J. Malik, “A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics,” ICCV 2001, vol. 2, pp. 416–423 vol.2, 2001.
- A. Floquet, S. Dutta, E. Soubies, D.-H. Pham, and D. Kouame, “Automatic tuning of denoising algorithms parameters without ground truth,” IEEE Signal Process. Lett., vol. 31, pp. 381–385, 2024.