Multimedia Tools and Applications

, Volume 76, Issue 5, pp 6355–6388 | Cite as

Sparse regularization method for the detection and removal of random-valued impulse noise



In this paper, we propose a novel two-stage algorithm for the detection and removal of random-valued impulse noise using sparse representations. The main aim of the paper is to demonstrate the strength of image inpainting technique for the reconstruction of images corrupted by random-valued impulse noise at high noise densities. First, impulse locations are detected by applying the combination of sparse denoising and thresholding, based on sparse and overcomplete representations of the corrupted image. This stage optimally selects threshold values so that the sum of the number of false alarms and missed detections obtained at a particular noise level is the minimum. In the second stage, impulses, detected in the first stage, are considered as the missing pixels or holes and subsequently these holes are filled-up using an image inpainting method. Extensive simulation results on standard gray scale images show that the proposed method successfully removes random-valued impulse noise with better preservation of edges and other details compared to the existing techniques at high noise ratios.


Random-valued impulse noise Impulse denoising Sparse representation Overcomplete dictionary Image inpainting 


  1. 1.
    Abreu E, Mitra S (1995) A signal-dependent rank ordered mean (SD-ROM) filter-a new approach for removal of impulses from highly corrupted images. Proceedings of ICASSP 4:2371–2374Google Scholar
  2. 2.
    Aharon M, Elad M, Bruckstein A (2006) K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans Signal Process 54 (11):4311–4322CrossRefGoogle Scholar
  3. 3.
    Bovik A, Huang T (1983) A generalization of median filtering using linear combinations of order statistics, IEEE Transactions on Acoustics. Speech Sign Proc 31 (6):1342–1350CrossRefMATHGoogle Scholar
  4. 4.
    Bovik A. (ed) (2000) Handbook of image and video processing, Elsevier Academic Press, AmsterdamGoogle Scholar
  5. 5.
    Boyd S, Vandenberghe L (2004) Convex Optimization. Cambridge University Press, New yorkCrossRefMATHGoogle Scholar
  6. 6.
    Bruckstein AM, Donoho DL, Elad M (2009) From sparse solutions of systems of equations to sparse modeling of signals. SIAM Rev 51(1):34–81MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Chan RH, Ho C, Nikolova M (2005) Salt-and-pepper noise removal by median-type noise detectors and detail preserving regularization. IEEE Trans Image Proc 14(10):1479–1485CrossRefGoogle Scholar
  8. 8.
    Chen SS, Donoho DL, Saunders MA (1998) Atomic decomposition by basis pursuit. SIAM J Sci Comput 20(1):33–61MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Chen T, Wu HR (2001) Adaptive impulse detection using center-weighted median filters. IEEE Sign Proc Lett 8(1):1–3CrossRefGoogle Scholar
  10. 10.
    Dawood H, Dawood H, Guo P (2015) Removal of random-valued impulse noise by local statistics. Multimedia Tools Appl 74(24):11485–11498CrossRefGoogle Scholar
  11. 11.
    Deka B, Bora PK (2011) Removal of random-valued impulse noise using sparse representation. In: Proceedings of National Conference on Communications, pp 1–5Google Scholar
  12. 12.
    Deng JL (1982) Control problems of grey system. Syst Control Lett 1:288–294MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Dong Y, Chan R, Xu S (2007) A detection statistic for random-valued impulse noise. IEEE Trans Image Process 16(4):1112–1120MathSciNetCrossRefGoogle Scholar
  14. 14.
    Dong Y, Xu S (2007) A new directional weighted median filter for removal of random-valued impulse noise. IEEE Sign Proc Lett 14(3):193–196CrossRefGoogle Scholar
  15. 15.
    Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289–1306MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Donoho D, Elad M, Temlyakov V (2006) Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans Inf Theory 52(1):6–18MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Elad M, Aharon M (2006) Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans Image Proc 15(12):3736–3745MathSciNetCrossRefGoogle Scholar
  18. 18.
    Elad M (2010) Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing, 1st ed. Springer Publishing Company, Incorporated, New YorkCrossRefMATHGoogle Scholar
  19. 19.
    Fantacci R, Tani A, Tarchi D (2010) Impulse Noise Mitigation Techniques for xDSL Systems in a Real Environment. IEEE Trans Cnsumer Electronics 56(4)Google Scholar
  20. 20.
    Gonzalez RC, Woods RE (2006) Digital image processing, 3rd Edition. Prentice-Hall, Inc, Upper Saddle RiverGoogle Scholar
  21. 21.
    Huang H, Zhu J (2010) Removal of salt-and-pepper noise based on compressed sensing. Electron Lett 46:1198–1199CrossRefGoogle Scholar
  22. 22.
    Jianhua S, Liangliang Z (2014) A local similarity pattern for removal of random valued impulse noise. J Multi 9(8):1054–1059Google Scholar
  23. 23.
    Ko SJ, Lee Y (1991) Center weighted median filters and their applications to image enhancement. IEEE Trans Circ Syst 38(9):984–993CrossRefGoogle Scholar
  24. 24.
    Mallat S, Zhang Z (1993) Matching pursuits with time frequency dictionaries. IEEE Trans Signal Process 41(12):3397–3415CrossRefMATHGoogle Scholar
  25. 25.
    Ng DKW (1994) Grey system and grey relational model. ACM SIGICE Bulletin 20(2):2–9MathSciNetCrossRefGoogle Scholar
  26. 26.
    Olshausen BA, Field DJ (1997) Sparse coding with an overcomplete basis set: A strategy employed by V1? Vis Res 37(23):3311–3325CrossRefGoogle Scholar
  27. 27.
    Pati Y, Rezaiifar R, Krishnaprasad P (1993) Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition. In: Proceedings of the 27th Annual Asilomer Conference on Signals, Systems, and Computers, pp 40–44Google Scholar
  28. 28.
    Rudin LI, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithm. Phys D 60:259–268MathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    Saikrishna P, Bora PK (2012) Detection and removal of fixed-valued impulse noise from images using sparse representations. In: Proceedings of International Conference on Signal Processing and Communications, pp 1–5Google Scholar
  30. 30.
    Saikrishna P, Bora PK (2013) Detection and removal of random-valued impulse noise from images using sparse representations. In: Proceedings of 20th IEEE International Conference Image Processing (ICIP), pp 1197–1201Google Scholar
  31. 31.
    Sattar F, Floreby L, Salomonsson L, Lovstrom B (1997) Image enhancement based on a nonlinear multiscale method. IEEE Trans Image Process 6(6):888–895CrossRefGoogle Scholar
  32. 32.
    Signal and Image Processing Institute of the University of Southern California, The USC-SIPI image database,
  33. 33.
    Starck J, Elad M, Donoho D (2005) Image decomposition via the combination of sparse representations and a variational approach. IEEE Trans Image Process 14:1570–1582MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Sun T, Neuvo Y (1994) Detail-preserving median based filters in image processing. Pattern Recogn Lett 15(4):341–347CrossRefGoogle Scholar
  35. 35.
    Tripathi AK, Ghanekar U, Mukhopadhyay S (2011) Switching median filter: advanced boundary discriminative noise detection algorithm. IET Image Proc 5 (7):598–610MathSciNetCrossRefGoogle Scholar
  36. 36.
    Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: From error visibility to structural similarity. IEEE Trans Image Process 13:600–612CrossRefGoogle Scholar
  37. 37.
    Zhang H, Zha ZJ, Yan S, Wang M, Chua TS (2012) Robust Non-negative Graph Embedding: Towards noisy data, unreliable graphs, and noisy labels. IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2012:2464–2471Google Scholar
  38. 38.
    Zhang H, Zha ZJ, Yang Y, Yan S, Chua TS (2014) Robust (semi) nonnegative graph embedding. IEEE Trans Image Process 23(7):2996–3012MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Computer Vision and Image Processing Laboratory, Department of Electronics and Communication EngineeringTezpur UniversityTezpurIndia

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