Citation: |
[1] |
S. Alliney, Digital filters as absolute norm regularizers, IEEE Trans. Signal Process., 40 (1992), 1548-1562.doi: 10.1109/78.139258. |
[2] |
P. Besbeas, I. D. Fies and T. Sapatinas, A comparative simulation study of wavelet shrinkage estimators for Poisson counts, International Statistical Review, 72 (2004), 209-237.doi: 10.1111/j.1751-5823.2004.tb00234.x. |
[3] |
P. Blomgren and T. F. Chan, Color TV: Total variation methods for restoration of vector-valued images, IEEE Trans. Image Process., 7 (1998), 304-309.doi: 10.1109/83.661180. |
[4] |
A. Bovik, "Handbook of Image and Video Processing," Academic Press, 2000. |
[5] |
X. Bresson and T. F. Chan, Fast dual minimization of the vectorial total variation norm and applications to color image processing, Inverse Problems and Imaging, 2 (2008), 455-484.doi: 10.3934/ipi.2008.2.455. |
[6] |
C. Brune, A. Sawatzky and M. Burger, Bregman-EM-TV methods with application to optical nanoscopy, LNCS, 5567 (2009), 235-246. |
[7] |
A. Caboussat, R. Glowinski and V. Pons, An augmented Lagrangian approach to the numerical solution of a non-smooth eigenvalue problem, J. Numer. Math., 17 (2009), 3-26.doi: 10.1515/JNUM.2009.002. |
[8] |
E. Candes, J. Romberg and T. Tao, Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Trans. Inform. Theory, 52 (2006), 489-509.doi: 10.1109/TIT.2005.862083. |
[9] |
J. L. Carter, "Dual Methods for Total Variation - Based Image Restoration," Ph.D thesis, UCLA, 2001. |
[10] |
A. Chambolle and P. L. Lions, Image recovery via total variation minimization and related problems, Numer. Math., 76 (1997), 167-188.doi: 10.1007/s002110050258. |
[11] |
A. Chambolle, An algorithm for total variation minimization and applications, J. Math. Imaging Vision, 20 (2004), 89-97.doi: 10.1023/B:JMIV.0000011321.19549.88. |
[12] |
R. Chan, C. W. Ho and M. Nikolova, Salt-and-pepper noise removal by median-type noise detector and detail-preserving regularization, IEEE Trans. Image Process., 14 (2005), 1479-1485.doi: 10.1109/TIP.2005.852196. |
[13] |
R. H. Chan and K. Chen, Multilevel algorithms for a Poisson noise removal model with total variation regularization, Int. J. Comput. Math., 84 (2007), 1183-1198.doi: 10.1080/00207160701450390. |
[14] |
T. F. Chan, G. H. Golub and P. Mulet, A nonlinear primal-dual method for total variation-based image restoration, SIAM J. Sci. Comput., 20 (1999), 1964-1977.doi: 10.1137/S1064827596299767. |
[15] |
T. Chan, A. Marquina and P. Mulet, High-order total variation-based image restoration, SIAM J. Sci. Comput., 22 (2000), 503-516.doi: 10.1137/S1064827598344169. |
[16] |
T. F. Chan, S. H. Kang and J. H. Shen, Total variation denoising and enhancement of color images based on the CB and HSV color models, J. Visual Commun. Image Repres., 12 (2001), 422-435.doi: 10.1006/jvci.2001.0491. |
[17] |
T. F. Chan and S. Esedoglu, Aspects of total variation regularized $L^1$ function approximation, SIAM J. Appl. Math., 65 (2005), 1817-1837.doi: 10.1137/040604297. |
[18] |
S. Chen, D. Donoho and M. A. Saunders, Atomic decomposition by basis pursuit, SIAM J. Sci. Comput., 20 (1998), pp. 33-61.doi: 10.1137/S1064827596304010. |
[19] |
T. Chen and H. R. Wu, Space variant median filters for the restoration of impulse noise corrupted images, IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., 48 (2001), 784-789. |
[20] |
Y. Dong, M. Hintermüller and M. Neri, An efficient primal-dual method for $L^1$TV image restoration, SIAM J. Imaging Sciences, 2 (2009), 1168-1189.doi: 10.1137/090758490. |
[21] |
D. L. Donoho, Compressed sensing, IEEE Trans. Inform. Theory, 52 (2006), 1289-1306.doi: 10.1109/TIT.2006.871582. |
[22] |
I. Ekeland and R. Témam, "Convex Analysis and Variational Problems," SIAM, 1999. |
[23] |
H. L. Eng and K. K. Ma, Noise adaptive soft-switching median filter, IEEE Trans. Image Process., 10 (2001), 242-251.doi: 10.1109/83.902289. |
[24] |
E. Esser, Applications of Lagrangian-based alternating direction methods and connections to split Bregman, UCLA CAM Report, cam09-31. Available from: ftp://ftp.math.ucla.edu/pub/camreport/cam09-31.pdf. |
[25] |
M. A. T. Figueiredo and J. M. Bioucas-Dias, Deconvolution of Poissonian images using variable splitting and augmented Lagrangian optimization, in "IEEE Workshop on Statistical Signal Processing," Cardiff, (2009), 733-736.doi: 10.1109/SSP.2009.5278459. |
[26] |
H. Y. Fu, M. K. Ng, M. Nikolova and J. L. Barlow, Efficient minimization methods of mixed l2-l1 and l1-l1 norms for image restoration, SIAM J. Sci. Comput., 27 (2006), 1881-1902.doi: 10.1137/040615079. |
[27] |
R. Glowinski and P. Le Tallec, "Augmented Lagrangians and Operator-Splitting Methods in Nonlinear Mechanics," SIAM, Philadelphia, 1989. |
[28] |
T. Goldstein and S. Osher, The split Bregman method for L1 regularized problems, SIAM J. Imaging Sciences, 2 (2009), 323-343.doi: 10.1137/080725891. |
[29] |
M. R. Hestenes, Multiplier and gradient methods, J. Optim. Theory and Appl., 4 (1969), 303-320.doi: 10.1007/BF00927673. |
[30] |
W. Hinterberger and O. Scherzer, Variational methods on the space of functions of bounded Hessian for convexification and denoising, Computing, 76 (2006), 109-133.doi: 10.1007/s00607-005-0119-1. |
[31] |
M. Hintermüller, K. Ito and K. Kunisch, The primal-dual active set strategy as a semismooth Newton method, SIAM J. Optim., 13 (2002), 865-888.doi: 10.1137/S1052623401383558. |
[32] |
Y. Huang, M. Ng and Y. Wen, A fast total variation minimization method for image restoration, SIAM Multi. Model. Simul., 7 (2008), 774-795.doi: 10.1137/070703533. |
[33] |
H. Hwang and R. A. Haddad, Adaptive median filters: New algorithms and results, IEEE Trans. Image Process., 4 (1995), 499-502.doi: 10.1109/83.370679. |
[34] |
C. Kervrann and A. Trubuil, An adaptive window approach for poisson noise reduction and structure preserving in confocal microscopy, in "Proc. International Symposium on Biomedical Imaging (ISBI'04)," Arlington, (2004), 788-791. |
[35] |
E. Kolaczyk, Wavelet shrinkage estimation of certain Poisson intensity signals using corrected thresholds, Statist. Sinica, 9 (1999), 119-135. |
[36] |
T. Le, R. Chartrand and T. J. Asaki, A variational approach to reconstructing images corrupted by Poisson noise, J. Math. Imaging Vision, 27 (2007), 257-263.doi: 10.1007/s10851-007-0652-y. |
[37] |
Y. Li and S. Osher, A new median formula with applications to PDE based denoising, Commun. Math. Sci., 7 (2009), 741-753. |
[38] |
M. Lysaker, A. Lundervold and X.-C. Tai, Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time, IEEE Trans. Image Process., 12 (2003), 1579-1590.doi: 10.1109/TIP.2003.819229. |
[39] |
M. Lysaker and X.-C. Tai, Iterative image restoration combining total variation minimization and a second order functional, Int'l J. Computer Vision, 2005. |
[40] |
P. Mrazek, J. Weickert and A. Bruhn, On robust estimations and smoothing with spatial and tonal kernels, in "Geometric Properties from Incomplete Data," Springer, (2006), 335-352.doi: 10.1007/1-4020-3858-8_18. |
[41] |
P. E. Ng and K. K. Ma, A switching median filter with boundary discriminative noise detection for extremely corrupted images, IEEE Trans. Image Process., 15 (2006), 1506-1516.doi: 10.1109/TIP.2005.871129. |
[42] |
M. Nikolova, Minimizers of cost-functions involving non-smooth data fidelity terms, SIAM J. Num. Anal., 40 (2002), 965-994.doi: 10.1137/S0036142901389165. |
[43] |
M. Nikolova, A variational approach to remove outliers and impulse noise, J. Math. Imaging Vision, 20 (2004), 99-120.doi: 10.1023/B:JMIV.0000011920.58935.9c. |
[44] |
V. Y. Panin, G. L. Zeng and G. T. Gullberg, Total variation regulated EM algorithm [SPECT reconstruction], IEEE Trans. Nucl. Sci., 46 (1999), 2202-2210.doi: 10.1109/23.819305. |
[45] |
G. Pok, J. C. Liu and A. S. Nair, Selective removal of impulse noise based on homogeneity level information, IEEE Trans. Image Process., 12 (2003), 85-92.doi: 10.1109/TIP.2002.804278. |
[46] |
M. J. D. Powell, A method for nonlinear constraints in minimization problems, in "Optimization"(ed. R. Fletcher), Academic Press, (1972), 283-298. |
[47] |
R. T. Rockafellar, A dual approach to solving nonlinear programming problems by unconstrained optimization, Mathematical Programming, 5 (1973), 354-373.doi: 10.1007/BF01580138. |
[48] |
L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), 259-268.doi: 10.1016/0167-2789(92)90242-F. |
[49] |
G. Sapiro and D. L. Ringach, Anisotropic diffusion of multivalued images with applications to color filtering, IEEE Trans. Image Process., 5 (1996), 1582-1586.doi: 10.1109/83.541429. |
[50] |
O. Scherer, Denoising with higher order derivatives of bounded variation and an application to parameter estimation, Computing, 60 (1998), 1-27.doi: 10.1007/BF02684327. |
[51] |
S. Setzer, Split Bregman algorithm, Douglas-Rachford splitting and frame shrinkage, LNCS, 5567 (2009), 464-476. |
[52] |
S. Setzer, G. Steidl and T. Teuber, Deblurring Poissonian images by split Bregman techniques, J. Visual Commun. Image Repres., accepted (2009). |
[53] |
L. A. Shepp and Y. Vardi, Maximum likelihood reconstruction for emission tomography, IEEE Trans. Medical Imaging, 1 (1982), 113-122.doi: 10.1109/TMI.1982.4307558. |
[54] |
X. C. Tai and C. L. Wu, Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model, LNCS, 5567 (2009), 502-513. |
[55] |
K. Timmermann and R. Novak, Multiscale modeling and estimation of Poisson processes with applications to photon-limited imaging, IEEE Trans. Inf. Theor., 45 (1999), 846-852.doi: 10.1109/18.761328. |
[56] |
Y. Wang, J. Yang, W. Yin and Y. Zhang, A new alternating minimization algorithm for total variation image reconstruction, SIAM J. Imaging Sciences, 1 (2008), 248-272.doi: 10.1137/080724265. |
[57] |
C. L. Wu and X. C. Tai, Augmented Lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and high order models, SIAM J. Imaging Sciences, 3 (2010), 300-339.doi: 10.1137/090767558. |
[58] |
J. F. Yang, W. T. Yin, Y. Zhang and Y. L. Wang, A fast algorithm for edge-preserving variational multichannel image restoration, SIAM J. Imaging Sciences, 2 (2009), 569-592.doi: 10.1137/080730421. |
[59] |
J. Yang, Y. Zhang and W. Yin, An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise, SIAM J. Sci. Comput., 31 (2009), 2842-2865.doi: 10.1137/080732894. |
[60] |
W. Yin, D. Goldfarb and S. Osher, Image cartoon-texture decomposition and feature selection using the total variation regularized $L^1$ functional, LNCS, 3752 (2005), 73-84. |
[61] |
W. Yin, D. Goldfarb and S. Osher, The total variation regularized $L^1$ model for multiscale decomposition, Multi. Model. Simul., 6 (2007), 190-211.doi: 10.1137/060663027. |
[62] |
W. T. Yin, S. Osher, D. Goldfarb and J. Darbon, Bregman iterative algorithms for compressend sensing and related problems, SIAM J. Imaging Sciences, 1 (2008), 143-168.doi: 10.1137/070703983. |
[63] |
W. T. Yin, Analysis and generalizations of the linearized Bregman method, SIAM J. Imaging Sciences, 3 (2010), 856-877.doi: 10.1137/090760350. |
[64] |
Y.-L. You and M. Kaveh, Fourth-order partial differential equation for noise removal, IEEE Trans. Image Process., 9 (2000), 1723-1730.doi: 10.1109/83.869184. |
[65] |
R. Zanella, P. Boccacci, L. Zanni and M. Bertero, Efficient gradient projection methods for edge-preserving removal of Poisson noise, Inverse Problems, 25 (2009). |
[66] |
M. Zhu and T. F. Chan, An efficient primal-dual hybrid gradient algorithm for total variation image restoration, UCLA CAM Report, cam08-34. Available from: ftp://ftp.math.ucla.edu/pub/camreport/cam08-34.pdf. |
[67] |
M. Zhu, S. J. Wright and T. F. Chan, Duality-based algorithms for total variation image restoration, Comput. Optim. Appl., (2008). Available from: http://www.springerlink.com/content/l2k84n130x6l4332/. |