A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising

Applied Mathematical Modelling

Volumn 35, Issue 5, 2011, Pages 2516-2528

  Jun, Zhang ^a   Zhihui, Wei ^a  

^a NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Fractional order derivative; Image denoising; Sobolev space; Staircase effect; Texture preserving

Indexed keywords

ALTERNATING PROJECTION ALGORITHM; BOUNDED VARIATIONS; DE-NOISING; DIFFERENT SCALE; FRACTIONAL-ORDER DERIVATIVE; IMAGE DE-NOISING; MULTISCALES; NEGATIVE SOBOLEV SPACES; NEW MODEL; NUMERICAL RESULTS; PEAK SIGNAL TO NOISE RATIO; PIECEWISE CONSTANT; PROJECTION ALGORITHMS; SOBOLEV SPACE; STAIRCASE EFFECT; TOTAL VARIATION; VARIATIONAL MODELS;

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; IMAGE PROCESSING; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NOISE POLLUTION CONTROL; SIGNAL TO NOISE RATIO; STAIRS; TEXTURES;

SOBOLEV SPACES;

EID: 78751611583     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2010.11.049     Document Type: Article

References (18)

1. Rudin L., Osher S., Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D 1992, 60(1-4):259-268.
2. Gilles J., Meyer Y. Properties of BV-G structures+textures decomposition models. Application to road detection in satellite images. IEEE Trans. Image Process. 2010, 9(11):2793-2800.
3. Meyer Y. Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The 15th Dean Jacqueline B. Lewis Memorial Lectures 2001, American Mathematical Society, Boston, MA.
4. Vese L., Osher S. Image denoising and decomposition with total variation minimization and oscillatory functions. J. Math. Imaging Vision 2004, 20:7-18.
5. -1 norm. Multi. Model. Simul. 2003, 1(3):349-370.
6. L. Linh, L. Vese, Image restoration and decomposition via bounded total variation and negative Hilbert-Sobolev space, UCLA CAM Report 05-33, 2005.
7. Aubert G., Aujol J.F. Modeling very oscillating signals. Application to image processing. Appl. Math. Opt. 2005, 51(2):163-182.
8. Chan T.F., Marquina A., Mulet P. High-order total variation based image restoration. SIAM J. Sci. Comput. 2000, 22(2):503-516.
9. You Y.L., Kaveh M. Fourth-order partial differential equations for noise removal. IEEE Trans. Image Process. 2000, 9(10):1723-1730.
10. Lysaker M., Lundervold A., Tai X.C. Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE Trans. Image Process. 2003, 12(12):1579-1590.
11. Lysaker M., Tai X.C. Iterative image restoration combining total variation minimization and a second-order functional. Int. J. Comput.Vis. 2006, 66(1):5-18.
12. Bai J., Feng X.C. Fractional-order anisotropic diffusion for image denoising. IEEE Trans. Image Process. 2007, 16(10):2492-2502.
13. Pu YF. Fractional calculus approach to texture of digital image, in: Proceedings of 8th International Conference on Signal Processing, IEEE, Beijing, 2006, pp. 1002-1006.
14. Pu Y.F. Application of fractional differential approach to digital image processing. J. Sichuan Univ. (Eng. Sci. Ed.) 2007, 39(3):124-132.
15. Pu Y.F. Fractional differential analysis for texture of digital image. J. Algorithms Comput. Technol. 2007, 1(3):357-380.
16. Pu Y.F., Wang W., Zhou J., Wang Y., Jia H. Fractional differential approach to detecting textural features of digital image and its fractional differential filter implementation. Sci. China Ser. F: Inform. Sci. 2008, 51(9):1319-1339.
17. Podlubny I. Fractional Differential Equations [M] 1999, Academic Press, New York.
18. Chambolle A. An algorithm for total variation minimization and applications. JMIV 2004, 20:89-97.