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STRUCTURE AND TEXTURE IMAGE INPAINTING USING SPARSE REPRESENTATIONS AND AN ITERATIVE CURVELET THRESHOLDING APPROACH

LINGLING JIANG

School of Science, Xidian University, Xi'an Shannxi, 710071, P. R. China

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XIANGCHU FENG

School of Science, Xidian University, Xi'an Shannxi, 710071, P. R. China

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, and

HAIQING YIN

School of Science, Xidian University, Xi'an Shannxi, 710071, P. R. China

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https://doi.org/10.1142/S0219691308002598Cited by:8 (Source: Crossref)

Abstract

Representing the image to be inpainted in an appropriate sparse dictionary, we introduce a novel method for the filling-in of structure and texture in regions of missing image information. In the morphological component analysis (MCA) inpainting approach, a TV penalty is added to better reduce ringing artifacts. However, the incorporation of TV penalty terms leads to PDE schemes that are numerically intensive. Inspired by the works of Daubechies–Teschke and Borup–Nielsen, we replace the TV term by a term. It results in an iterative curvelet thresholding scheme for the structure image inpainting. In the whole inpainting process, an alternative approach is presented to layer inpainting. Experimental results show the performance of the algorithm.

Keywords:

AMSC: 47A52, 49M30, 65J22

References

C. Ballesteret al., IEEE Trans. Image Process. Appl. 10(8), 1200 (2001), DOI: 10.1109/83.935036. Crossref, Web of Science, Google Scholar
M. Bertalmioet al., Image inpainting, Proc. ACM Conf. Computer Graphics (SIGGRAPH 2000), ed. K. Akeley (ACM Press, 2000) pp. 417–424. Google Scholar
T. Chan and J. Shen, SIAM J. Appl. Math. 62(3), 1019 (2002). Web of Science, Google Scholar
T. Chan and J. Shen, J. Vis. Commun. Image Representation 12(4), 436 (2002), DOI: 10.1006/jvci.2001.0487. Crossref, Web of Science, Google Scholar
L.-Y. Wei and M. Levoy, Fast texture synthesis using tree structured vector quantization, Proc. ACM Conf. Computer Graphics (SIGGRAPH 2000), ed. K. Akeley (ACM Press, 2000) pp. 479–488. Google Scholar
M. Ashikhmin, Synthesizing natural textures, Proc. 2001 ACM Symp. Interactive 3D Graphics (ACM Press, 2001) pp. 217–226. Google Scholar
R. Paget and D. Longstaff, Texture Synthesis via a nonparametric Markov random field, Proc. DICTA 95, Digital Image Computing: Techniques and Applications1, eds. A. Maeder and B. Lovell (Australian Pattern Recognition Society, 1995) pp. 547–552. Google Scholar
A. Efros and T. Leung, Texture synthesis by non parametric sampling, IEEE Int. Conf. Computer Vision (ICCV'99) (1999) pp. 1033–1038. Google Scholar
S. D. Rane, G. Sapiro and M. Bertalmio, IEEE Trans. Image Process. 12(3), 296 (2003), DOI: 10.1109/TIP.2002.804264. Crossref, Web of Science, Google Scholar
M. Bertalmioet al., IEEE Trans. Image Process. 12(8), 882 (2003), DOI: 10.1109/TIP.2003.815261. Crossref, Web of Science, Google Scholar
J. Jia and C.-K. Tang, Image repairing: Robust image synthesis by adaptive ND tensor voting, Proc. IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'03)1, eds. C. Dyer and Perona (IEEE Computer Society, 2003) pp. 643–650. Google Scholar
M. Eladet al., Appl. Comput. Harmon. Anal. 19(3), 340 (2005), DOI: 10.1016/j.acha.2005.03.005. Crossref, Web of Science, Google Scholar
J.-L. Starck, M. Elad and D. L. Donoho, IEEE Trans. Image Process. 14(10), 340 (2005), DOI: 10.1109/TIP.2005.852206. Google Scholar
L. Borup and M. Nielsen, J. Fourier Anal. Appl. 13(1), 39 (2007), DOI: 10.1007/s00041-006-6024-y. Crossref, Web of Science, Google Scholar
S. Chen, D. Donoho and M. Saunder, SIAM J. Sci. Comput. 20, 33 (1998), DOI: 10.1137/S1064827596304010. Crossref, Web of Science, Google Scholar
L. Rudin, S. Osher and E. Fatemi, Phys. D 60, 259 (1992), DOI: 10.1016/0167-2789(92)90242-F. Crossref, Web of Science, Google Scholar
E. J. Candès and D. L. Donoho, Curves and Surface Fitting, eds. A. Cohen, C. Rabut and L. L. Schumaker (Vanderbilt Univ. Press, 2000) pp. 105–120. Google Scholar
E. J. Candès and D. L. Donoho, Comm. Pure Appl. Math. 57(2), 219 (2004). Crossref, Web of Science, Google Scholar
Y. J. Huet al., Springer Lecture Notes in Computer Science 2939 (Springer, 2003) pp. 86–100. Google Scholar
E. B. Fox, Detection and localization of aerosol releases from sparse sensor measurements, M.Eng. Thesis, Cambridge University (2005) . Google Scholar
N. Kingsbury, R. Soc. Lond. Philos. Trans. Ser. A 357, 2543 (1999), DOI: 10.1098/rsta.1999.0447. Crossref, Web of Science, Google Scholar
I. Daubechies and G. Teschke, Appl. Comput. Harmon. Anal. 19(1), 1 (2005), DOI: 10.1016/j.acha.2004.12.004. Crossref, Web of Science, Google Scholar
M. Li, B. Hao and X. Feng, Int. J. Wavelets Multiresolut. Inf. Process. 6(1), 83 (2008), DOI: 10.1142/S0219691308002239. Link, Web of Science, Google Scholar
I. Daubechies, M. Defrise and C. DeMol, Comm. Pure Appl. Math. 57, 1413 (2005), DOI: 10.1002/cpa.20042. Crossref, Web of Science, Google Scholar
A. Bruce, S. Sardy and P. Tseng, Block coordinate relaxation methods for nonparametric signal de-noising, Proc. SPIE 3391 (1998) pp. 75–86. Google Scholar