Iteratively solving linear inverse problems under general convex constraints

Inverse Problems and Imaging

Volumn 1, Issue 1, 2007, Pages 29-46

  Daubechies, Ingrid ^a   Teschke, Gerd ^b   Vese, Luminita ^c  

^a PRINCETON UNIVERSITY   (United States)

^b Department of Jazz Drums and Improvisation   (Germany)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Besov and BV restoration; Generalized shrinkage; Landweber iteration; Linear inverse problems

Indexed keywords

EID: 78649765600     PISSN: 19308337     EISSN: 19308345     Source Type: Journal    
DOI: 10.3934/ipi.2007.1.29     Document Type: Article

References (22)

1. G. Aubert and J.-F. Aujol, Modeling very oscillating signals. Application to image processing, Applied Mathematics and Optimization, 51(2) (2005), 163–182.
2. G. Aubert and L. Vese, A variational method in image recovery, SINUM, 34(5) (1997), 1948–1979.
3. S. Boyd and L. Vandenberghe, “Convex Optimization,” Cambridge Univ. Press, Cambridge, 2005.
4. A. Chambolle, An Algorithm for total variation minimization and applications, Journal of Mathematical Imaging and Vision, 20(1-2) (2004), 89–97.
5. A. Chambolle and P.-L. Lions, Image recovery via total variation minimization and related problems , Numerische Mathematik, 76(2) (1997), 167–188.
6. P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward–backward splitting, Multiscale Modeling and Simulation, 4(4) (2005), 1168–1200.
7. I. Daubechies and M. Defrise and C. DeMol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Comm. Pure Appl. Math, 57 (2004), 1413–1541.
8. I. Daubechies and G. Teschke, Wavelet–based image decomposition by variational functionals, Proc. SPIE Vol. 5266 (F. Truchetet, Ed.), Wavelet Applications in Industrial Processing (2004), 94–105.
9. I. Daubechies and G. Teschke, Variational image restoration by means of wavelets: simultaneous decomposition, deblurring and denoising, Applied and Computational Harmonic Analysis, 19(1) (2005), 1–16.
10. F. Demengel and R. Temam, Convex functions of a measure and applications, Indiana University Mathematics Journal, 33(5) (1984), 673–709.
11. S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Transactions on PAMI, 6(6) (1984), 721–741.
12. D. Geman and G. Reynolds, Constrained restoration and the recovery of discontinuities, IEEE Transactions on PAMI, 14(3) (1992), 367–383.
13. J-B. Hiriart-Urruty and C. Lemaréchal, “Convex Analysis and Minimization Algorithms I,” Springer, Berlin, 1993.
14. Y. Meyer, “Oscillating Patterns in Image Processing and Nonlinear Evolution Equations,” University Lecture Series Volume 22, AMS, 2002.
15. Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73 (1967), 591–597.
16. −1 norm, Multiscale Modeling and Simulation, 1(3) (2003), 349–370.
17. L. Vese and S. Osher, Modeling textures with total variation minimization and oscillating patterns in image processing, Journal of Scientific Computing, 19(1-3) (2003), 553–572.
18. P. Perona and J. Malik, Scale space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intell., 12 (1990), 629–639.
19. R. T. Rockafellar and R. J-B. Wets, “Variational Analysis,” Springer, Berlin, 1998.
20. L.I. Rudin and S. Osher, Total variation based image restoration with free local constraints, Proceedings. ICIP-94, 1 (1994), 31–35.
21. L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60(1-4) (1992), 259–268.
22. L. Vese, A study in the BV space of a denoising-deblurring variational problem , Applied Mathematics and Optimization, 44(2) (2001), 131–161.