Abstract
In this paper, we propose a high-order total variation model to restore blurred and noisy images with spatially adapted regularization parameter selection. The proposed model can substantially reduce the staircase effect, while preserving sharp jump discontinuities (edges) in the restored images. We employ an alternating direction minimization method for the proposed model. Some numerical results are given to illustrate the effectiveness of the proposed method.
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References
Andrew, H., Hunt, B.: Digital Image Restoration. Prentice-Hall, Englewood Cliffs (1977)
Chan, T.F., Shen, J.H.: Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods. SIAM, Philadelphia (2005)
Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D 60, 259–268 (1992)
Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imag. Vis. 20, 89–97 (2004)
Wang, Y.L., Yang, J.F., Yin, W.T., Zhang, Y.: A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imag. Sci. 1(3), 248–272 (2008)
Vogel, C.R.: Computational Methods for Inverse Problems. SIAM, Philadelphia (2002)
Beck, A., Teboulle, M.: Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans. Image Process. 18(11), 2419–2434 (2009)
Lefkimmiatis, S., Bourquard, A., Unser, M.: Hessian-based norm regularization for image restoration with biomedical applications. IEEE Trans. Image Process. 21(3), 983–995 (2012)
Lysker, M., Tai, X.C.: Iterative image restoration combining total varition minimization and a second-order functional. Int. J. Comput. Vis. 66(1), 5–18 (2006)
Hansen, P.C., Nagy, J.G. O’Leary, D.P.: Deblurring Images: Matrices, Spectra, and Filtering. SIAM, Philadelphia (2006)
Strong, D., Aujol, J.F., Chan, T.F.: Scale Recognition, Regularization Parameter Selection, and Meyer’s G Norm in Total Variation Regularization, Technical Report. UCLA, Los Angeles (2005)
Almansa, A., Ballester, C., Caselles, V., Haro, G.: A TV based restoration model with local constraints. J. Sci. Comput. 34(3), 209–236 (2008)
Dong, Y.Q., Hintermüller, M., Rincon-Camacho, M.M.: Automated regularization parameter selection in multi-scale total variation models for image restoration. J Math. Imag. Vis. 40(1), 82–104 (2011)
Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: From error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)
Acknowledgments
This research is supported by NSFC (10871034, 61170311), Sichuan Province Science and Technology. Research Project (12ZC1802) and Research Project of Jiangsu Province (12KJD110001, 1301064B), China Postdoctoral Science Foundation funded project (2013M540454).
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Jiang, L., Huang, J., Lv, XG., Liu, J. (2014). High-Order Total Variation-Based Image Restoration with Spatially Adapted Parameter Selection. In: Patnaik, S., Li, X. (eds) Proceedings of International Conference on Computer Science and Information Technology. Advances in Intelligent Systems and Computing, vol 255. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1759-6_9
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DOI: https://doi.org/10.1007/978-81-322-1759-6_9
Publisher Name: Springer, New Delhi
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