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A Scratch Covering Algorithm Using Affine Projection Method

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Abstract

The restoration process attempts to recover an image that has been degraded and for this many approaches were used in time, but the filling-in with its two variants, apriori pattern and undamaged near border pattern are widely used. In this paper a new algorithm for “inpainting” a scratch of an image is proposed. The proposed algorithm uses a transfer of the information from the unaffected area to the damaged area by the bias of a dynamic pondered affine projection algorithm. The theoretical link between image recovery problem and the convex feasibility problem is discussed in this paper. More, the convergence of the proposed algorithm is proved.

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References

  1. Aryadarsh, S., Dhanya, M., Neevan, R.: Image completion using Criminisi algorithm. Glob. Res. Dev. J. Eng. 1(6), 116–122 (2016)

    Google Scholar 

  2. Bauschke, H.H., Borwein, J.M.: On projection algorithms for solving convex feasibility problems. Soc. Ind. Appl. Math. Rev. 38(3), 367–426 (1996)

    MathSciNet  MATH  Google Scholar 

  3. Bertalmio, M., Vese, L., Sapiro, G., Osher, S.: Simultaneous structure and texture image inpainting. IEEE Trans. Image Process. 12(8), 882–889 (2003)

    Article  Google Scholar 

  4. Bertalmio, M., Sapiro, G., Caselles, V., Ballester, C.: Image inpainting. ACM Comput. Graph. (SIGGRAPH 2002) 417–424 (2000)

  5. Chen, A.: The inpainting of hyperspectral images: a survey and adaptation to hyperspectral data. Image Signal Process. Remote Sens. 18, 85371K–85371K (2012)

    Google Scholar 

  6. Combettes, P.L.: Advances in Imaging and Electron Physics 95, pp. 155–270. Academic Press, New York (1996)

    Book  Google Scholar 

  7. Combettes, P.L.: Applied Mathematics and Optimization 35, pp. 311–330. Springer-Verlag, New York (1997)

    Google Scholar 

  8. Combettes, P.L.: Convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections. IEEE Trans. Image Process. 6(4), 493–506 (1997)

    Article  Google Scholar 

  9. Criminisi, A., Perez, P., Toyama, K.: Region filling and object removal by exemplar-based image inpainting. IEEE Trans. Image Process. 13(9), 1200–1212 (2004)

    Article  Google Scholar 

  10. Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. J. Theor. Biol. 36, 105–117 (1972)

    Article  Google Scholar 

  11. Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. J. Theor. Biol. 29, 471–481 (1970)

    Article  Google Scholar 

  12. Gubin, L.G., Polyak, B.T., Raik, E.V.: The method of projections for finding the common point of convex sets. USSR Comput. Math. Math. Phys. 7, 1–24 (1967)

    Article  Google Scholar 

  13. Mustafa, B., Trajkovik, V., Davcev, D.: Missing data correction in still images using multi-resolution analysis. J. Comput. Inf. Technol. 1, 1–5 (2007)

    Article  Google Scholar 

  14. Telea, A.: An image inpainting technique based on the fast marching method. J. Graph. Tools 9(1), 23–34 (2012)

    Article  Google Scholar 

  15. Xiaowei, S., Zhengkai, L., Houqiang, L.: An image inpainting approach based on the Poisson equation. In: Proceedings of the Second International Conference on Document Image Analysis for Libraries (DIAL06) 27–28, pp. 368–372 (2006)

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Correspondence to Irina Maria Artinescu.

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Artinescu, I.M., Mafteiu-Scai, L.O. A Scratch Covering Algorithm Using Affine Projection Method. Math.Comput.Sci. 12, 235–246 (2018). https://doi.org/10.1007/s11786-018-0342-8

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  • DOI: https://doi.org/10.1007/s11786-018-0342-8

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