A new algorithm framework for image inpainting in transform domain.

*(English)*Zbl 1352.68274##### MSC:

68U10 | Computing methodologies for image processing |

65K10 | Numerical optimization and variational techniques |

94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |

##### Software:

RecPF
PDF
BibTeX
XML
Cite

\textit{F. Li} and \textit{T. Zeng}, SIAM J. Imaging Sci. 9, No. 1, 24--51 (2016; Zbl 1352.68274)

Full Text:
DOI

##### References:

[1] | C. Ballester, M. Bertalmio, V. Caselles, G. Sapiro, and J. Verdera, Filling-in by joint interpolation of vector fields and gray levels, IEEE Trans. Image Process., 10 (2001), pp. 1200–1211. · Zbl 1037.68771 |

[2] | M. Bertalmio, G. Sapiro, V. Caselles, and C. Ballester, Image inpainting, in Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, ACM Press/Addison-Wesley, Reading, MA, 2000, pp. 417–424. |

[3] | A. L. Bertozzi, S. Esedoglu, and A. Gillette, Inpainting of binary images using the Cahn–Hilliard equation, IEEE Trans. Image Process., 16 (2007), pp. 285–291. · Zbl 1279.94008 |

[4] | D. P. Bertsekas, A. Nedi, A. E. Ozdaglar, et al., Convex Analysis and Optimization, Athena Scientific, Belmont, MA, 2003. |

[5] | K. Bredies and D. A. Lorenz, Iterated hard shrinkage for minimization problems with sparsity constraints, SIAM J. Sci. Comput., 30 (2008), pp. 657–683. · Zbl 1170.46067 |

[6] | M. Burger, A. Sawatzky, and G. Steidl, First Order Algorithms in Variational Image Processing, preprint, arXiv:1412.4237, 2014. |

[7] | J.-F. Cai, R. H. Chan, L. Shen, and Z. Shen, Convergence analysis of tight framelet approach for missing data recovery, Adv. Comput. Math., 31 (2009), pp. 87–113. · Zbl 1172.94309 |

[8] | J.-F. Cai, R. H. Chan, and Z. Shen, A framelet-based image inpainting algorithm, Appl. Comput. Harmon. Anal., 24 (2008), pp. 131–149. · Zbl 1135.68056 |

[9] | A. Chambolle, An algorithm for total variation minimization and applications, J. Math. Imaging Vision, 20 (2004), pp. 89–97. · Zbl 1366.94048 |

[10] | A. Chambolle and T. Pock, A first-order primal-dual algorithm for convex problems with applications to imaging, J. Math. Imaging Vision, 40 (2011), pp. 120–145. · Zbl 1255.68217 |

[11] | R. H. Chan, Y.-W. Wen, and A. M. Yip, A fast optimization transfer algorithm for image inpainting in wavelet domains, IEEE Trans. Image Process., 18 (2009), pp. 1467–1476. · Zbl 1371.94075 |

[12] | R. H. Chan, J. Yang, and X. Yuan, Alternating direction method for image inpainting in wavelet domains, SIAM J. Imaging Sci., 4 (2011), pp. 807–826. · Zbl 1234.68448 |

[13] | T. F. Chan, J. Shen, and H.-M. Zhou, Total variation wavelet inpainting, J. Math. Imaging Vision, 25 (2006), pp. 107–125. |

[14] | Y. Chen, W. Hager, F. Huang, D. Phan, X. Ye, and W. Yin, Fast algorithms for image reconstruction with application to partially parallel MR imaging, SIAM J. Imaging Sci., 5 (2012), pp. 90–118. · Zbl 1247.90212 |

[15] | Y. Chen, G. Lan, and Y. Ouyang, Optimal primal-dual methods for a class of saddle point problems, SIAM J. Optim., 24 (2014), pp. 1779–1814. · Zbl 1329.90090 |

[16] | E. Corman and X. Yuan, A generalized proximal point algorithm and its convergence rate, SIAM J. Optim., 24 (2014), pp. 1614–1638. · Zbl 1311.90099 |

[17] | A. Criminisi, P. Pérez, and K. Toyama, Region filling and object removal by exemplar-based image inpainting, IEEE Trans. Image Process., 13 (2004), pp. 1200–1212. |

[18] | K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, Image denoising by sparse 3-d transform-domain collaborative filtering, IEEE Trans. Image Process., 16 (2007), pp. 2080–2095. |

[19] | A. Danielyan, V. Katkovnik, and K. Egiazarian, BM3D frames and variational image deblurring, IEEE Trans. Image Process., 21 (2012), pp. 1715–1728. · Zbl 1373.94096 |

[20] | Y. Dong, M. Hintermüller, and M. Neri, An efficient primal-dual method for \(l^1\) tv image restoration, SIAM J. Imaging Sci., 2 (2009), pp. 1168–1189. · Zbl 1187.68653 |

[21] | M. Elad and M. Aharon, Image denoising via sparse and redundant representations over learned dictionaries, IEEE Trans. Image Process., 15 (2006), pp. 3736–3745. |

[22] | M. Elad, B. Matalon, and M. Zibulevsky, Image denoising with shrinkage and redundant representations, in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Vol. 2, 2006, pp. 1924–1931. |

[23] | M. Elad, J.-L. Starck, P. Querre, and D. L. Donoho, Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA), Appl. Comput. Harmonic Analy., 19 (2005), pp. 340–358. · Zbl 1081.68732 |

[24] | M.-J. Fadili, J.-L. Starck, and F. Murtagh, Inpainting and zooming using sparse representations, Comput. J., 52 (2009), pp. 64–79. |

[25] | E. Ghadimi, A. Teixeira, I. Shames, and M. Johansson, Optimal parameter selection for the alternating direction method of multipliers (admm): Quadratic problems, IEEE Trans. Automat. Control, 60 (2015), pp. 644–658. · Zbl 1360.90182 |

[26] | T. Goldstein and S. Osher, The split Bregman method for \(l1\)-regularized problems, SIAM J. Imaging Sci., 2 (2009), pp. 323–343. · Zbl 1177.65088 |

[27] | O. G. Guleryuz, Nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising—Part II: Adaptive algorithms, IEEE Trans. Image Process., 15 (2006), pp. 555–571. |

[28] | W. Guo, J. Qin, and W. Yin, A new detail-preserving regularization scheme, SIAM J. Imaging Sci., 7 (2014), pp. 1309–1334. · Zbl 1299.65130 |

[29] | E. T. Hale, W. Yin, and Y. Zhang, Fixed-point continuation for \(\{L}\_1\)-minimization: Methodology and convergence, SIAM J. Optim., 19 (2008), pp. 1107–1130. · Zbl 1180.65076 |

[30] | S. Hawe, M. Kleinsteuber, and K. Diepold, Analysis operator learning and its application to image reconstruction, in Proceedings of the IEEE Trans. Image Process., 22 (2013), pp. 2138–2150. · Zbl 1373.94161 |

[31] | B. He, Y. You, and X. Yuan, On the convergence of primal-dual hybrid gradient algorithm, SIAM J. Imaging Sci., 7 (2014), pp. 2526–2537. · Zbl 1308.90129 |

[32] | R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, UK, 2012. |

[33] | Y.-M. Huang, M. K. Ng, and Y.-W. Wen, A new total variation method for multiplicative noise removal, SIAM J. Imaging Sci., 2 (2009), pp. 20–40. · Zbl 1187.68655 |

[34] | F. Li and T. Zeng, A universal variational framework for sparsity based image inpainting, IEEE Trans. Image Process., 23 (2014), pp. 4242–4254. · Zbl 1374.94201 |

[35] | T. Lin, S. Ma, and S. Zhang, On the Global Linear Convergence of the Admm with Multi-Block Variables, preprint, arXiv:1408.4266, 2014. |

[36] | S. Ma, W. Yin, Y. Zhang, and A. Chakraborty, An efficient algorithm for compressed mr imaging using total variation and wavelets, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2008, pp. 1–8. |

[37] | M. Nikolova, M. K. Ng, and C.-P. Tam, Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction, IEEE Trans. Image Process., 19 (2010), pp. 3073–3088. · Zbl 1371.94277 |

[38] | J. Nocedal and S. J. Wright, Penalty and Augmented Lagrangian Methods, Springer, New York, 2006. |

[39] | I. Ram, M. Elad, and I. Cohen, Image processing using smooth ordering of its patches, IEEE Trans. Image Process., 22 (2013), pp. 2764–2774. · Zbl 1373.94339 |

[40] | S. Setzer, Operator splittings, bregman methods and frame shrinkage in image processing, Int. J. Comput. Vision, 92 (2011), pp. 265–280. · Zbl 1235.68314 |

[41] | J. Shen and T. F. Chan, Mathematical models for local nontexture inpaintings, SIAM J. Appl. Math., 62 (2002), pp. 1019–1043. · Zbl 1050.68157 |

[42] | J. Shen, S. H. Kang, and T. F. Chan, Euler’s elastica and curvature-based inpainting, SIAM J. Appl. Math., 63 (2003), pp. 564–592. · Zbl 1028.68185 |

[43] | X.-C. Tai, S. Osher, and R. Holm, Image inpainting using a TV-Stokes equation, in Image Processing Based on Partial Differential Equations, Springer, New York, 2007, pp. 3–22. |

[44] | Y. Wang, J. Yang, W. Yin, and Y. Zhang, A new alternating minimization algorithm for total variation image reconstruction, SIAM J. Imaging Sci., 1 (2008), pp. 248–272. · Zbl 1187.68665 |

[45] | Y.-W. Wen, R. H. Chan, and A. M. Yip, A primal–dual method for total-variation-based wavelet domain inpainting, IEEE Trans. Image Process., 21 (2012), pp. 106–114. · Zbl 1372.94268 |

[46] | A. Wong and J. Orchard, A nonlocal-means approach to exemplar-based inpainting, in Proceedings of the 15th IEEE International Conference on Image Processing, 2008, pp. 2600–2603. |

[47] | Z. Xu and J. Sun, Image inpainting by patch propagation using patch sparsity, IEEE Trans. Image Process., 19 (2010), pp. 1153–1165. · Zbl 1371.94424 |

[48] | X. Ye and H. Zhou, Fast total variation wavelet inpainting via approximated primal-dual hybrid gradient algorithm, Inverse Problems Imaging, 7 (2013), pp. 1031–1050. · Zbl 1273.65094 |

[49] | G. Yu, G. Sapiro, and S. Mallat, Solving inverse problems with piecewise linear estimators: From Gaussian mixture models to structured sparsity, IEEE Trans. Image Process., 21 (2012), pp. 2481–2499. · Zbl 1373.94471 |

[50] | X. Zhang, M. Burger, X. Bresson, and S. Osher, Bregmanized nonlocal regularization for deconvolution and sparse reconstruction, SIAM J. Imaging Sci., 3 (2010), pp. 253–276. · Zbl 1191.94030 |

[51] | X. Zhang and T. F. Chan, Wavelet inpainting by nonlocal total variation, Inverse Problems Imaging, 4 (2010), pp. 191–210. · Zbl 1185.42040 |

[52] | X.-L. Zhao, W. Wang, T.-Y. Zeng, T.-Z. Huang, and M. K. Ng, Total variation structured total least squares method for image restoration, SIAM J. Sci. Comput., 35 (2013), pp. B1304–B1320. · Zbl 1287.65014 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.