Advertisement

A Non-local Method for Robust Noisy Image Completion

  • Wei Li
  • Lei Zhao
  • Duanqing Xu
  • Dongming Lu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8692)

Abstract

The problem of noisy image completion refers to recovering an image from a random subset of its noisy intensities. In this paper, we propose a non-local patch-based algorithm to settle the noisy image completion problem following the methodology “grouping and collaboratively filtering”. The target of “grouping” is to form patch matrices by matching and stacking similar image patches. And the “collaboratively filtering” is achieved by transforming the tasks of simultaneously estimating missing values and removing noises for the stacked patch matrices into low-rank matrix completion problems, which can be efficiently solved by minimizing the nuclear norm of the matrix with linear constraints. The final output is produced by synthesizing all the restored patches. To improve the robustness of our algorithm, we employ an efficient and accurate patch matching method with adaptations including pre-completion and outliers removal, etc. Experiments demonstrate that our approach achieves state-of-the-art performance for the noisy image completion problem in terms of both PSNR and subjective visual quality.

Keywords

Matrix Completion Nuclear Norm Completion Problem Similar Patch Corrupted Image 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Supplementary material

978-3-319-10593-2_5_MOESM1_ESM.pdf (21.3 mb)
Electronic Supplementary Material(21,773 KB)

References

  1. 1.
    Barcelos, C.A.Z., Batista, M.A.: Image restoration using digital inpainting and noise removal. Image and Vision Computing 25(1), 61–69 (2007)CrossRefGoogle Scholar
  2. 2.
    Barnes, C., Shechtman, E., Finkelstein, A., Goldman, D.B.: Patchmatch: a randomized correspondence algorithm for structural image editing. In: SIGGRAPH (2009)Google Scholar
  3. 3.
    Beck, A., Teboulle, M.: Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE TIP 18(11), 2419–2434 (2009)MathSciNetGoogle Scholar
  4. 4.
    Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms, with a new one. Multiscale Modeling and Simulation 4(2), 490–530 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Candès, E.J., Plan, Y.: Matrix completion with noise. Proceedings of the IEEE 98(6), 925–936 (2010)CrossRefGoogle Scholar
  6. 6.
    Coifman, R.R., Donoho, D.L.: Translation-invariant de-noising. Springer (1995)Google Scholar
  7. 7.
    Criminisi, A., Pérez, P., Toyama, K.: Region filling and object removal by exemplar-based image inpainting. IEEE TIP 13(9), 1200–1212 (2004)Google Scholar
  8. 8.
    Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE TIP 16(8), 2080–2095 (2007)MathSciNetGoogle Scholar
  9. 9.
    Dahl, J., Hansen, P.C., Jensen, S.H., Jensen, T.L.: Algorithms and software for total variation image reconstruction via first-order methods. Numerical Algorithms 53(1), 67–92 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Donoho, D.L., Johnstone, J.M.: Ideal spatial adaptation by wavelet shrinkage. Biometrika 81(3), 425–455 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE TIP 15(12), 3736–3745 (2006)MathSciNetGoogle Scholar
  12. 12.
    Goldluecke, B., Strekalovskiy, E., Cremers, D.: The natural vectorial total variation which arises from geometric measure theory. SIAM Journal on Imaging Sciences 5(2), 537–563 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Goldstein, T., Osher, S.: The split bregman method for l1-regularized problems. SIAM Journal on Imaging Sciences 2(2), 323–343 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Ji, H., Liu, C., Shen, Z., Xu, Y.: Robust video denoising using low rank matrix completion. In: CVPR (2010)Google Scholar
  15. 15.
    Keshavan, R.H., Montanari, A., Oh, S.: Matrix completion from noisy entries. Journal of Machine Learning Research 11(2057-2078), 1 (2010)MathSciNetGoogle Scholar
  16. 16.
    Kokaram, A.C.: On missing data treatment for degraded video and film archives: a survey and a new bayesian approach. IEEE TIP 13(3), 397–415 (2004)Google Scholar
  17. 17.
    Kokaram, A.C., Godsill, S.J.: Mcmc for joint noise reduction and missing data treatment in degraded video. IEEE TSP 50(2), 189–205 (2002)Google Scholar
  18. 18.
    Komodakis, N., Tziritas, G.: Image completion using efficient belief propagation via priority scheduling and dynamic pruning. IEEE TIP 16(11), 2649–2661 (2007)MathSciNetGoogle Scholar
  19. 19.
    Lin, Z., Chen, M., Ma, Y.: The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices. UIUC Technical Report UILUENG-09-2215 (2010)Google Scholar
  20. 20.
    Mairal, J., Bach, F., Ponce, J., Sapiro, G., Zisserman, A.: Non-local sparse models for image restoration. In: ICCV (2009)Google Scholar
  21. 21.
    Mairal, J., Elad, M., Sapiro, G.: Sparse representation for color image restoration. IEEE TIP 17(1), 53–69 (2008)MathSciNetGoogle Scholar
  22. 22.
    Peyré, G., Bougleux, S., Cohen, L.: Non-local regularization of inverse problems. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part III. LNCS, vol. 5304, pp. 57–68. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  23. 23.
    Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena 60(1), 259–268 (1992)CrossRefzbMATHGoogle Scholar
  24. 24.
    Simakov, D., Caspi, Y., Shechtman, E., Irani, M.: Summarizing visual data using bidirectional similarity. In: CVPR (2008)Google Scholar
  25. 25.
    Subrahmanyam, G., Aravind, R.A., Recursive, R.: framework for joint inpainting and de-noising of photographic films. JOSA A 27(5), 1091–1099 (2010)CrossRefGoogle Scholar
  26. 26.
    Wang, X., Mirmehdi, M.: Archive film restoration based on spatiotemporal random walks. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part V. LNCS, vol. 6315, pp. 478–491. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  27. 27.
    Wang, Y., Yang, J., Yin, W., Zhang, Y.: A new alternating minimization algorithm for total variation image reconstruction. SIAM Journal on Imaging Sciences 1(3), 248–272 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    Wei, L.Y., Levoy, M.: Fast texture synthesis using tree-structured vector quantization. In: SIGGRAPH (2000)Google Scholar
  29. 29.
    Yan, M.: Restoration of images corrupted by impulse noise and mixed gaussian impulse noise using blind inpainting. SIAM Journal on Imaging Sciences 6(3), 1227–1245 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  30. 30.
    Zhu, M., Wright, S.J., Chan, T.F.: Duality-based algorithms for total-variation-regularized image restoration. Computational Optimization and Applications 47(3), 377–400 (2010)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Wei Li
    • 1
  • Lei Zhao
    • 1
  • Duanqing Xu
    • 1
  • Dongming Lu
    • 1
  1. 1.Zhejiang UniversityHangzhouChina

Personalised recommendations