CCCV 2015: Computer Vision pp 335-343 | Cite as
An Accelerated Two-Step Iteration Hybrid-norm Algorithm for Image Restoration
Abstract
Linear inverse problem is an important solution frame to solve image restoration. This paper develops an accelerated two-step iteration hybrid-norm reconstruction algorithm, exhibiting much faster convergence rate and better image than iteration shrinkage/thresholding based L1 norm algorithm. In the proposed method, hybrid norm model is built for image restoration objective function. Two-step iteration accelerates objective minimization optimization. Two-step iteration hybrid-norm algorithm converges to a minimizer of hybrid-norm objective function, for a given range of values of its parameters. Numerical examples are presented to validate that the effectiveness of the proposed algorithm is experimentally confirmed on problems of restoration with missing samples.
Keywords
Hybrid-norm Image restoration Compressive sensing Two-step iterationPreview
Unable to display preview. Download preview PDF.
References
- 1.Andrews, H., Hunt, B.: Digital Image Restoration. Prentice-Hall, Englewood Cliffs (1977)MATHGoogle Scholar
- 2.Bertero, M., Boccacci, P.: Introduction to Inverse Problems in Imaging. Bristol, UK (1998)CrossRefMATHGoogle Scholar
- 3.Katsaggelos, A.: Digital Image Restoration. Springer, New York (2012)Google Scholar
- 4.Archer, G., Titterington, D.: On Bayesian/regularization Methods for Image Restoration. IEEE Trans. Image Process. 4(3), 989–995 (1995)CrossRefGoogle Scholar
- 5.Daubechies, I., Defriese, M., De Mol, C.: An Iterative Thresholding Algorithm for Linear Inverse Problems with a Sparsity Constraint. Commun. Pure Appl. Math. 57(11), 1413–1457 (2004)MathSciNetCrossRefMATHGoogle Scholar
- 6.Beck, A., Teboulle, M.: A Fast Iterative Shrinkage-thresholding Algorithm for Linear Inverse Problems. SIAM J. Imaging Sciences 2(1), 183–202 (2009)MathSciNetCrossRefMATHGoogle Scholar
- 7.Bioucas-Das, J., Figueiredo, M.: A New Twist: Two Step Iterative Shrinkage/thresholding Algorithms for Image Restoration. IEEE Trans. Image Process. 16(12), 2992–3004 (2007)MathSciNetCrossRefGoogle Scholar
- 8.Bioucas-Dias, J., Figueiredo, M.: Two-step Algorithms for Linear Inverse Problems with Non-quadratic Regularization. In: IEEE Int. Conf. Image Process., San Antonio, TX (2007)Google Scholar
- 9.Wang, Y., Liang, D., Chang, Y., Ying, L.: A Hybrid Total-Variation Minimization Approach to Compressed Sensing. IEEE International Symposium on Biomedical Imaging, Barcelona, Spain, pp. 74–77 (2012)Google Scholar
- 10.Chen, X., Michael Ng, K., Zhang, C.: Non-Lipschitz Lp-regularization and Box Constrained Model for Image Restoration. IEEE Trans. on Imaging Process. 21(12), 4709–4720 (2012)CrossRefGoogle Scholar
- 11.Dong, W., Zhang, L., Shi, G., Li, X.: Nonlocally Centralized Sparse Representation for Image Restoration. IEEE Trans. on Imaging Process. 22(4), 1620–1630 (2013)MathSciNetCrossRefGoogle Scholar
- 12.Liang, D., Ying, L.: A Hybrid L0-L1 Minimization Algorithm for Compressed Sensing MRI. In: Proceedings of International Society of Magnetic Resonance in Medicine Scientific Meeting (2010)Google Scholar