Non-Lipschitz lp-regularization and box constrained model for image restoration

IEEE Transactions on Image Processing

Volumn 21, Issue 12, 2012, Pages 4709-4721

  Chen, Xiaojun ^a   Ng, Michael K ^b   Zhang, Chao ^c  

^a HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^b HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^c BEIJING JIAOTONG UNIVERSITY   (China)

Author keywords

Box constraints; image restoration; non Lipschitz; nonsmooth and nonconvex; regularization

Indexed keywords

BOX CONSTRAINTS; CLOSED CONTOURS; CONSTRAINED MODELS; EXPLICIT FORM; LOCAL MINIMIZER; NON-CONVEX MINIMIZATION; NON-LIPSCHITZ; NON-SMOOTH; NONCONVEX; NUMERICAL EXAMPLE; PIECEWISE CONSTANT; POSITIVE CONSTANT; PRIORI INFORMATION; REGULARIZATION; THEORETICAL RESULT;

CONSTRAINED OPTIMIZATION; RESTORATION;

IMAGE RECONSTRUCTION;

EID: 84869480932     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2012.2214051     Document Type: Article

References (22)

1. M. K. Ng, R. H. Chan, and W. Tang, "A fast algorithm for deblurring models with Neumann boundary conditions," SIAM J. Sci. Comput., vol. 21, no. 3, pp. 965-994, 1999.
2. G. Golub, P. Hansen, and D. O'Leary, "Tikhonov regularization and total least squares," SIAM J. Matrix Anal., vol. 21, no. 1, pp. 185-194, 1999.
3. L. I. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica, vol. 60, nos. 1-4, pp. 259-268, 1992.
4. N. Paragios, C. Chen, and O. Faugeras, Handbook of Mathematical Models in Computer Vision. New York: Springer-Verlag, 2006.
5. X. Chen and W. Zhou, "Smoothing nonlinear conjugate gradient method for image restoration using nonsmooth nonconvex minimization," SIAM J. Imag. Sci., vol. 3, no. 4, pp. 765-790, 2010.
6. M. Nikolova, "Minimizers of cost-functions involving nonsmooth datafidelity terms. Application to the processing of outliers," SIAM J. Numer. Anal., vol. 40, no. 3, pp. 965-994, 2002.
7. M. Nikolova, "A variational approach to remove outliers and impulse noise," J. Math. Imag. Vis., vol. 20, nos. 1-2, pp. 99-120, 2004.
8. M. Nikolova, M. K. Ng, S. Zhang, and W. Ching, "Efficient reconstruction of piecewise constant images using nonsmooth nonconvex minimization," SIAM J. Imag. Sci., vol. 1, no. 1, pp. 2-25, 2008.
9. M. Nikolova, "Analysis of the recovery of edges in images and signals by minimizing nonconvex regularized least-squares," Multiscale Model. Simul., vol. 4, no. 3, pp. 960-991, 2005.
10. M. Nikolova, M. K. Ng, and C. P. Tam, "Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction," IEEE Trans. Image Process., vol. 19, no. 12, pp. 3073-3088, Dec. 2010.
11. R. Gonzalez and R. Woods, Digital Image Processing, 3rd ed. Upper Saddle River, NJ: Pearson Education, 2008.
12. A. Jain, Fundamentals of Digital Image Processing. Englewood Cliffs, NJ: Prentice-Hall, 1989.
13. M. R. Banham and A. K. Katsaggelos, "Digital image restoration," IEEE Signal Process. Mag., vol. 14, no. 2, pp. 24-41, Mar. 1997.
14. M. Hanke, J. Nagy, and C. Vogel, "Quasi-Newton approach to nonnegative image restorations," Linear Algebra Appl., vol. 316, nos. 1-3, pp. 223-236, 2000.
15. J. Nagy and Z. Strakos, "Enforcing nonnegativity in image reconstruction algorithms," in Mathematical Modeling, Estimation, and Imaging, vol. 4121, D. C. Wilson, Eds. Bellingham, WA: SPIE, 2000, pp. 182- 190.
16. M. Hong, T. Stathaki, and A. Katsaggelos, "Iterative regularized image restoration using local constraints," in Proc. IEEE Workshop Nonlinear Signal Image Process., Sep. 1997, pp. 1-4.
17. D. Krishnan, L. Ping, and A. M. Yip, "A primal-dual active-set method for non-negativity constrained total variation deblurring problems," IEEE Trans. Image Process., vol. 16, no. 11, pp. 2766-2777, Nov. 2007.
18. D. Geman, Random Fields and Inverse Problems in Imaging (Lecture Notes in Mathematics). Berlin, Germany: Springer-Verlag, 1990.
19. D. Geman and G. Reynolds, "Constrained restoration and the recovery of discontinuities," IEEE Trans. Pattern Anal. Mach. Intell., vol. 14, no. 3, pp. 367-383, Mar. 1992.
20. D. Geman and C. Yang, "Nonlinear image recovery with half-quadratic regularization," IEEE Trans. Image Process., vol. 4, no. 7, pp. 932-946, Jul. 1995.
21. C. Zhang and X. Chen, "Smoothing projected gradient method and its application to stochastic linear complementarity problems," SIAM J. Optim., vol. 20, no. 2, pp. 627-649, 2009.
22. X. Chen, F. Xu, and Y. Ye, "Lower bound theory of nonzero entries in solutions of 2-p minimization," SIAM J. Sci. Comput., vol. 32, no. 5, pp. 2832-2852, 2010.