Analysis of half-quadratic minimization methods for signal and image recovery

SIAM Journal on Scientific Computing

Volumn 27, Issue 3, 2006, Pages 937-966

  Nikolova, Mila ^a   Ng, Michael K ^b,c  

^a Inserm   (France)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

^c HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

Author keywords

Convergence analysis; Half quadratic regularization; Inverse problems; Maximum a posteriori estimation; Optimization; Preconditioning; Signal and image restoration; Variational methods

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; INVERSE PROBLEMS; ITERATIVE METHODS; OPTIMIZATION; SIGNAL THEORY;

CONVERGENCE ANALYSIS; HALF-QUADRATIC REGULARIZATION; MAXIMUM A POSTERIORI ESTIMATION; PRECONDITIONING; SIGNAL AND IMAGE RESTORATION; VARIATIONAL METHODS;

IMAGE RECONSTRUCTION;

EID: 33646596282     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/030600862     Document Type: Article

References (31)

1. R. ACAR AND C. VOGEL, Analysis of bounded variation penalty methods for ill-posed problems, IEEE Trans. Image Process., 10 (1994), pp. 1217-1229.
2. G. AUBERT AND P. KORNPROBST, Mathematical Problems in Image Processing, Springer-Verlag, Berlin, 2002.
3. G. AUBERT AND L. VESE, A variational method in image recovery, SIAM J. Numer. Anal., 34 (1997), pp. 1948-1979.
4. M. BLACK AND A. RANGARAJAN, On the unification of line processes, outlier rejection, and robust statistics with applications to early vision, Internat. J. Computer Vision, 19 (1996), pp. 57-91.
5. G. BOUMAN AND K. SAUER, A generalized Gaussian image model for edge-preserving MAP estimation, IEEE Trans. Image Process., 2 (1993), pp. 296-310.
6. R. H. CHAN AND M. K. NG, Conjugate gradient methods for Toeplitz systems, SIAM Rev., 38 (1996), pp. 427-482.
7. P. CHARBONNIER, L. BLANC-FÉRAUD, G. AUBERT, AND M. BARLAUD, Two deterministic halfquadratic regularization algorithms for computed imaging, in Proceedings of IEEE ICIP, Vol. 2, 1994, pp. 168-172.
8. P. CHARBONNIER, L. BLANC-FÉFRAUD, G. AUBERT, AND M. BARLAUD, Deterministic edgepreserving regularization in computed imaging, IEEE Trans. Image Process., 6 (1997), pp. 298-311.
9. P. G. CIARLET, Introduction à l'analyse numérique matricielle et à l'optimisation, Collection mathématiques appliquées pour la maîtrise, Masson, Paris, 1990.
10. L. D. COHEN, Auxiliary variables and two-step iterative algorithms in computer vision problems, J. Math. Imaging Vision, 6 (1996), pp. 376-386.
11. A. H. DELANEY AND Y. BRESLER, Globally convergent edge-preserving regularized reconstruction: An application to limited-angle tomography, IEEE Trans. Image Process., 7 (1998), pp. 204-221.
12. G. DEMOMENT, Image reconstruction and restoration: Overview of common estimation structures and problems, IEEE Trans. Acoustics Speech Signal Process., 37 (1989), pp. 2024-2036.
13. D. GEMAN AND G. REYNOLDS, Constrained restoration and the recovery of discontinuities, IEEE Trans. Pattern Anal. Machine Intelligence, 14 (1992), pp. 367-383.
14. D. GEMAN AND C. YANG, Nonlinear image recovery with half-quadratic regularization, IEEE Trans. Image Process., 4 (1995), pp. 932-946.
15. S. GEMAN AND D. GEMAN, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Trans. Pattern Anal. Machine Intelligence, 6 (1984), pp. 721-741.
16. R. GLOWINSKI, J. LIONS, AND R. TRÉMOLIèRES, Analyse numérique des inéquations variationnelles, Vol. 1, 1st ed., Dunod, Paris, 1976.
17. P. J. GREEN, Bayesian reconstructions from emission tomography data using a modified EM algorithm, IEEE Trans. Medical Imaging, 9 (1990), pp. 84-93.
18. J.-B. HIRIART-URRUTY AND C. LEMARÉCHAL, Convex Analysis and Minimization Algorithms, Vol. I, Springer-Verlag, Berlin, 1996.
19. J. IDIER, Convex half-quadratic criteria and interacting auxiliary variables for image restoration, IEEE Trans. Image Process., 10 (2001), pp. 1001-1009.
20. T. KAILATH AND A. H. SAVED, Displacement structure: Theory and applications, SIAM Rev., 37 (1995), pp. 297-386.
21. P. KORNPROBST, R. DERICHE, AND G. AUBERT, Image sequence analysis via partial differential equations, J. Math. Imaging Vision, 11 (1999), pp. 5-26.
22. S. LI, Markov Random Field Modeling in Computer Vision, 1st ed., Springer-Verlag, New York, 1995.
23. M. NG, R. CHAN, T. CHAN, AND A. YIP, Cosine transform preconditioned for high resolution image reconstruction, Linear Algebra Appl., 316 (2000), pp. 89-104.
24. M. K. NG, R. H. CHAN, AND W.-C. TANG, A fast algorithm for deblurring models with Neumann boundary conditions, SIAM J. Sci. Comput., 21 (1999), pp. 851-866.
25. M. NIKOLOVA, Local strong homogeneity of a regularized estimator, SIAM J. Appl. Math., 61 (2000), pp. 633-658.
26. J. ORTEGA AND W. RHEINBOLDT, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
27. R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
28. L. RUDIN, S. OSHER, AND E. FATEMI, Nonlinear total variation based noise removal algorithms, Phys. D, 60 (1992), pp. 259-268.
29. A. TARANTOLA, Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation, Elsevier-North Holland, Amsterdam, 1987.
30. S. TEBOUL, L. BLANC-FÉRAUD, G. AUBERT, AND M. BARLAUD, Voriational approach for edge-preserving regularization using coupled PDE's, IEEE Trans. Image Process., 7 (1998), pp. 387-397.
31. A. TIKHONOV AND V. ARSENIN, Solutions of Ill-Posed Problems, Winston, Washington, DC, 1977.