Preserving details while restoring images highly corrupted by impulsive salt and pepper noise remains a challenging problem. The authors proposed an algorithm based on radial basis functions (RBFs) interpolation which estimates the intensities of corrupted pixels by their neighbours. In this algorithm, intensity values of noisy pixels in the corrupted image are first estimated using RBFs. Next, the image is smoothed. The proposed algorithm can effectively remove the highly dense, impulsive salt and pepper noise. Experimental results show the superiority of the proposed algorithm both in noise suppression and details preservation in comparison to the recent similar methods. Extensive simulations show better results measured by peak signal-to-noise ratio and structural similarity index, especially when the image is corrupted by very highly dense impulse noise.

References

1. 1)
  - 13. Schulte, S., Nachtegael, M., De Witte, V., et al: ‘A fuzzy impulse noise detection and reduction method’, IEEE Trans. Image Process., 2006, 15, pp. 1153–1162.
2. 2)
  - 15. Aggarwal, H.K., Majumdar, A.: ‘Generalized synthesis and analysis prior algorithms with application to impulse denoising’. Proc. of the 2014 Indian Conf. Computer Vision Graphics and Image Processing, 2014, p. 10.
3. 3)
  - 5. Hwang, H., Haddad, R.: ‘Adaptive median filters: new algorithms and results’, IEEE Trans. Image Process., 1995, 4, pp. 499–502.
4. 4)
  - 24. Gao, X.-W.: ‘The radial integration method for evaluation of domain integrals with boundary-only discretization’, Eng. Anal. Bound. Elem., 2002, 26, pp. 905–916.
5. 5)
  - 19. Rojas, R., Rodriguez, P.: ‘Spatially adaptive total variation image denoising under salt and pepper noise’. 19th European Signal Processing Conf., 2011, 2011, pp. 278–282.
6. 6)
  - 4. Cai, J.-F., Chan, R.H., Shen, L., et al: ‘Convergence analysis of tight framelet approach for missing data recovery’, Adv. Comput. Math., 2009, 31, pp. 87–113.
7. 7)
  - 2. Wang, S.-S., Wu, C.-H.: ‘A new impulse detection and filtering method for removal of wide range impulse noises’, Pattern Recognit., 2009, 42, pp. 2194–2202.
8. 8)
  - 6. Jourabloo, A., Feghahati, A., Jamzad, M.: ‘New algorithms for recovering highly corrupted images with impulse noise’, Sci. Iranica, 2012, 19, pp. 1738–1745.
9. 9)
  - 22. Wang, Z., Bovik, A.C., Sheikh, H.R., et al: ‘Image quality assessment: from error visibility to structural similarity’, IEEE Trans. Image Process., 2004, 13, pp. 600–612.
10. 10)
  - 21. Hawkins, D.M.: ‘The problem of overfitting’, J. Chem. Inf. Comput. Sci., 2004, 44, pp. 1–12.
11. 11)
  - 8. Wu, J., Tang, C.: ‘An efficient decision-based and edge-preserving method for salt-and-pepper noise removal’, Pattern Recognit. Lett., 2011, 32, pp. 1974–1981.
12. 12)
  - 28. Franke, R.: ‘Scattered data interpolation: tests of some methods’, Math. Comput., 1982, 38, pp. 181–200.
13. 13)
  - 10. Nair, M.S., Revathy, K., Tatavarti, R.: ‘An improved decision-based algorithm for impulse noise removal’. Image and Signal Processing, 2008, CISP'08. Congress on, 2008, pp. 426–431.
14. 14)
  - 23. Sun, T., Neuvo, Y.: ‘Detail-preserving median based filters in image processing’, Pattern Recognit. Lett., 1994, 15, pp. 341–347.
15. 15)
  - 18. Veerakumar, S.E.T., Vennila, I.: ‘High density impulse noise removal using modified switching bilateral filter’, Int. J. Circuits Syst. Signal Process., 2012, 6, (3), pp. 189–196.
16. 16)
  - 12. Chen, P.-Y., Lien, C.-Y.: ‘An efficient edge-preserving algorithm for removal of salt-and-pepper noise’, IEEE Signal Process. Lett., 2008, 15, pp. 833–836.
17. 17)
  - 17. Ahmed, F., Das, S.: ‘Removal of high-density salt-and-pepper noise in images with an iterative adaptive fuzzy filter using alpha-trimmed mean’, IEEE Trans. Fuzzy Syst., 2014, 22, pp. 1352–1358.
18. 18)
  - 25. Fasshauer, G.E., Zhang, J.G.: ‘On choosing ‘optimal’ shape parameters for RBF approximation’, Numer. Algorithms, 2007, 45, pp. 345–368.
19. 19)
  - 26. Trefethen, L.N., Bau, D.III: ‘Numerical linear algebra’, vol. 50 (Siam, 1997).
20. 20)
  - 7. Esakkirajan, S., Veerakumar, T., Subramanyam, A.N., et al: ‘Removal of high density salt and pepper noise through modified decision based unsymmetric trimmed median filter’, IEEE Signal Process., 2011, 18, pp. 287–290.
21. 21)
  - 9. Srinivasan, K., Ebenezer, D.: ‘A new fast and efficient decision-based algorithm for removal of high-density impulse noises’, IEEE Signal Process. Lett., 2007, 14, pp. 189–192.
22. 22)
  - 1. Chan, R.H., Ho, C.-W., Nikolova, M.: ‘Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization’, IEEE Trans. Image Process., 2005, 14, pp. 1479–1485.
23. 23)
  - 27. Rippa, S.: ‘An algorithm for selecting a good value for the parameter c in radial basis function interpolation’, Adv. Comput. Math., 1999, 11, pp. 193–210.
24. 24)
  - 3. Bovik, A.C.: ‘Handbook of image and video processing’ (Academic Press, 2010).
25. 25)
  - 16. Wang, Z., Zhang, D.: ‘Progressive switching median filter for the removal of impulse noise from highly corrupted images’, IEEE Trans. Circuits Syst. II, Analog Digital Signal Process., 1999, 46, pp. 78–80.
26. 26)
  - 20. Toh, K.K.V., Isa, N.A.M., Ashidi, N.: ‘Noise adaptive fuzzy switching median filter for salt-and-pepper noise reduction’, IEEE Signal Process. Lett., 2010, 17, pp. 281–284.
27. 27)
  - 14. Hosseini, H., Hessar, F., Marvasti, F.: ‘Real-time impulse noise suppression from images using an efficient weighted-average filtering’, IEEE Signal Process. Lett., 2015, 22, pp. 1050–1054.
28. 28)
  - 11. Chen, S., Yang, X., Cao, G.: ‘Impulse noise suppression with an augmentation of ordered difference noise detector and an adaptive variational method’, Pattern Recognit. Lett., 2009, 30, pp. 460–467.

Restoring highly corrupted images by impulse noise using radial basis functions interpolation

References

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