Alternating method based on framelet l₀-norm and TV regularization for image restoration

References

• Andrews HC, Hunt BR. Digital image restoration. Englewood Cliffs (NJ): Prentice-Hall; 1977.
   Google Scholar
• Bovik A, Gibson JD. Handbook of image and video process. ACM Digital Library Press; 2005.
   Google Scholar
• Chan TF, Shen J. Image processing and analysis: variational, PDE, wavelet, and stochastic methods. Philadelphia (PA): SIAM; 2005.
   Google Scholar
• Chen HS, Wang CY, Song Y, et al. Split Bregmanized anisotropic total variation model for image deblurring. J Vis Commun Image R. 2015;31:282–293. doi: 10.1016/j.jvcir.2015.07.004
   Web of Science ®Google Scholar
• Jia TT, Shi YY, Zhu YG, et al. An image restoration model combining mixed L1/L2 fidelity term. J Vis Commun Image R. 2016;38:461–473. doi: 10.1016/j.jvcir.2016.03.022
   Google Scholar
• Liu J, Shi Y, Zhu Y. A fast and robust algorithm for image restoration with periodic boundary conditions. J Comput Anal Appl. 2014;17(3):524–538.
   Google Scholar
• Wang Y, Yang J, Yin W, et al. A new alternating minimization algorithm for total variation image reconstruction. SIAM J Imag Sci. 2008;1(3):248–272. doi: 10.1137/080724265
   Web of Science ®Google Scholar
• Zhang T, Gao QL, Tan GS. Texture preserving image restoration with dyadic bounded mean oscillating constraints. IEEE Signal Process Lett. 2015;22(3):322–326. doi: 10.1109/LSP.2014.2359002
   Web of Science ®Google Scholar
• Rudin L, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithm. Phys D. 1992;60:259–268. doi: 10.1016/0167-2789(92)90242-F
   Web of Science ®Google Scholar
• Aubert G, Vese L. A variational method in image recovery. SIAM J Numer Anal. 1997;34(5):1948–1979. doi: 10.1137/S003614299529230X
   Web of Science ®Google Scholar
• Rudin L, Osher S. Total variation based image restoration with free local constraints. IEEE Int Conf Image Process. 1994;1:31–35. doi: 10.1109/ICIP.1994.413269
   Google Scholar
• Chambolle A. An algorithm for total variation minimization and applications. J Math Imaging Vis. 2004;20(1–2):89–97.
   Web of Science ®Google Scholar
• Chan TF, Golub GH, Mulet P. A nonlinear primal-dual method for total variation-based image restoration. SIAM J Sci Comput. 1999;20(6):1964–1977. doi: 10.1137/S1064827596299767
   Web of Science ®Google Scholar
• Hintermuller M, Stadler G. An infeasible primal-dual algorithm for TV-based Inf-convolution-type image restoration. SIAM J Sci Comput. 2006;28(1):1–23. doi: 10.1137/040613263
   Web of Science ®Google Scholar
• Vogel C, Oman M. Fast, robust total variation-based reconstruction of noisy, blurring images. IEEE Trans Image Process. 1998;7(6):813–824. doi: 10.1109/83.679423
   PubMed Web of Science ®Google Scholar
• Vogel C, Oman M. Iterative methods for total variation denoising. SIAM J Sci Comput. 1996;17(1):227–238. doi: 10.1137/0917016
   Web of Science ®Google Scholar
• Beck A, Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J Imaging Sci. 2009;2(1):183–202. doi: 10.1137/080716542
   Web of Science ®Google Scholar
• Combettes PL, Luo J. An adaptive level set method for nondifferentiable constrained image recovery. IEEE Trans Image Process. 2002;11:1295–1304. doi: 10.1109/TIP.2002.804527
   PubMed Web of Science ®Google Scholar
• Goldfarb D, Yin W. Second-order cone programming methods for total variation based image restoration. SIAM J Sci Comput. 2005;27:622–645. doi: 10.1137/040608982
   Web of Science ®Google Scholar
• Li Y, Santosa F. A computational algorithm for minimizing total variation in image restoration. IEEE Trans Image Process. 1996;5:987–995. doi: 10.1109/83.503914
   PubMed Web of Science ®Google Scholar
• Weiss P, Blanc-Feraud L, Aubert G. Efficient schemes for total variation minimization under constraints in image processing. SIAM J Sci Comput. 2009;31:2047–2080. doi: 10.1137/070696143
   Web of Science ®Google Scholar
• Goldstein T, Osher S. The split Bregman method for L1-regularization problems. SIAM J Imag Sci. 2009;2(2):323–343. doi: 10.1137/080725891
   Web of Science ®Google Scholar
• Osher S, Burger M, Goldfarb D, et al. An iterative regularization method for total variation-based image restoration. Multiscale Model Simul. 2005;4(2):460–489. doi: 10.1137/040605412
   Web of Science ®Google Scholar
• Yang J, Yin W, Zhang Y, et al. A fast algorithm for edge-preserving variational multichannel image restoration. SIAM J Imag Sci. 2009;2(2):569–592. doi: 10.1137/080730421
   Web of Science ®Google Scholar
• Yin W, Osher S, Goldfarb D, et al. Bregman iterative algorithms for L1-minimization with applications to compressed sensing. SIAM J Imag Sci. 2008;1(1):143–168. doi: 10.1137/070703983
   Web of Science ®Google Scholar
• Micchelli CA, Shen LX, Xu YS. Proximity algorithms for image models: denoising. Inverse Probl. 2011;24(4):1–30.
   Google Scholar
• Huang YM, Ng MK, Wen YW. A fast total variation minimization method for image restoration. Multiscale Model Simul. 2008;7(2):774–795. doi: 10.1137/070703533
   Web of Science ®Google Scholar
• Dong B, Zhang Y. An efficient algorithm for l0 minimizaton in wavelet frame based image restoration. J Sci Comput. 2013;54(2):350–368. doi: 10.1007/s10915-012-9597-4
   Google Scholar
• Bao CL, Dong B, Hou LK, et al. Image restoration by minimizing zero norm of wavelet frame coefficients. Inverse Probl. 2016;32(11):115004. doi: 10.1088/0266-5611/32/11/115004
   Web of Science ®Google Scholar
• Pan J, Hu Z, Su Z, et al. Deblurring text images via L0-Regularized intensity and gradient prior. IEEE Conf Comput Vis Pattern Recog. 2014;2901–2908.
   Google Scholar
• Yuan G, Ghanem B. l0TV: a new method for image restoration in the presence of impulse noise. Comput Vis Pattern Recog. 2015;5369–5377.
   Google Scholar
• Zhang N, Li Q. On optimal solutions of the constrained l0 regularization and its penalty problem. Inverse Probl. 2017;33(2):1–28. doi: 10.1088/1361-6420/33/2/025010
   Google Scholar
• Zhang Y, Dong B, Lu Z. l0 Minimization for wavelet frame based image restoration. Math Comput. 2011;82(282):995–1015. doi: 10.1090/S0025-5718-2012-02631-7
   Google Scholar
• Cai JF, Osher S, Shen Z. Split Bregman method and frame based image restoration. Multisc Model Simul. 2009;8(2):337–369. doi: 10.1137/090753504
   Web of Science ®Google Scholar
• Cai JF, Ji H, Liu CQ, et al. Framelet-based blind motion deblurring from a single image. IEEE Trans Image Process. 2012;21(2):562–572. doi: 10.1109/TIP.2011.2164413
   PubMed Web of Science ®Google Scholar
• Daubechies I, Defrise M, De Mol C. An iterative threshoding algorithm for linear inverse problems with a sparsity constraint. Commun Pure Appl Math. 2004;57:1413–1457. doi: 10.1002/cpa.20042
   Web of Science ®Google Scholar
• Gabay D, Mercier B. A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Comput Math Appl. 1976;2(1):17–40. doi: 10.1016/0898-1221(76)90003-1
   Google Scholar
• Hestenes M. Multiplier and gradient methods. J Optim Theory Appl. 1969;4(5):303–320. doi: 10.1007/BF00927673
   Google Scholar