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Image denoising based on non-local means filter and its method noise thresholding

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Abstract

Non-local means filter uses all the possible self-predictions and self-similarities the image can provide to determine the pixel weights for filtering the noisy image, with the assumption that the image contains an extensive amount of self-similarity. As the pixels are highly correlated and the noise is typically independently and identically distributed, averaging of these pixels results in noise suppression thereby yielding a pixel that is similar to its original value. The non-local means filter removes the noise and cleans the edges without losing too many fine structure and details. But as the noise increases, the performance of non-local means filter deteriorates and the denoised image suffers from blurring and loss of image details. This is because the similar local patches used to find the pixel weights contains noisy pixels. In this paper, the blend of non-local means filter and its method noise thresholding using wavelets is proposed for better image denoising. The performance of the proposed method is compared with wavelet thresholding, bilateral filter, non-local means filter and multi-resolution bilateral filter. It is found that performance of proposed method is superior to wavelet thresholding, bilateral filter and non-local means filter and superior/akin to multi-resolution bilateral filter in terms of method noise, visual quality, PSNR and Image Quality Index.

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Abbreviations

BF:

Bilateral filter

DCHWT:

Discrete cosine harmonic wavelet transform

IQI:

Image Quality Index

MRBF:

Multi-resolution bilateral filter

MSE:

Mean-squared error

NL means:

Non-local means

NLFMT:

Non-local means filter and its method noise thresholding

SURE:

Stein unbiased risk estimator

WT:

Wavelet transform

References

  1. Gonzalez, R.C., Woods, R.E.: Digital Image Process. Pearson Education (Singapore) Pte. Ltd, Delhi (2004)

    Google Scholar 

  2. Ghazel, M.: Adaptive Fractal and Wavelet Image Denoising. PhD Thesis, Department of Electrical& Computer Engineering, University of Waterloo, Ontario (2004)

  3. Chang, S.G., Yu, B., Vetterli, M.: Adaptive wavelet thresholding for image denoising and compression. In: IEEE Trans. Image Process. 9(9), 1532–1546 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. Jansen, M.: Wavelet Thresholding and Noise Reduction. PhD Thesis, Department of Computer Science, Katholieke Universiteit Leuven, Heverlee (2000)

  5. Şendur, L., Selesnick, I.W.: Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency. In: IEEE Trans. Signal Process. 50(11), 2744–2756 (2002)

    Article  Google Scholar 

  6. Fang, H.-T., Huang, D.-S.: Wavelet de-noising by means of trimmed thresholding. In: Proceedings of the 5th World Congress on Intelligent Control and Automation, vol. 2, pp. 1621–1624. Hangzhou, P. R. China (2004)

  7. Zong, X., Laine, A.F., Geiser, E.A., Wilson, D.C.: De-Noising and contrast enhancement via wavelet shrinkage and nonlinear adaptive gain. Wavelet applications III. In: Proceedings of SPIE, vol. 2762, Orlando, pp. 566–574 (1996)

  8. Marpe, D., Cycon, H. L., Zander, G., Barthel, K.-U.: Context-based denoising of images using iterative wavelet thresholding. In: Proceedings of SPIE on Visual Communications and Image Process. vol. 4671, pp. 907–914 (2002)

  9. Cristobal, G., Cuesta, J., Cohen, L.: Image Filtering and denoising through the scale transform. In: IEEE Proceedings of International Symposium on Time-Frequency and Time-Scale Analysis, Pittsburgh, pp. 617–620 (1998)

  10. Donoho, D.L., Johnstone, I.M.: Ideal spatial adaptation via wavelet shrinkage. Biometrika 81(3), 425–455 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  11. Donoho, D.L.: Denoising by soft thresholding. In: IEEE Trans Inf. Theory 41(3), 613–627 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  12. Chang, S.G., Yu, B., Vetterli, M.: Spatially adaptive thresholding with context modeling for image denoising. In: IEEE Trans Image Process. 9(9), 1522–1531 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  13. Pizurica, A., Philips, W.: Estimating the probability of the presence of a signal of interest in multiresolution single and multiband image denoising. In: IEEE Trans Image Process 15(3), 654–665 (2006)

    Article  Google Scholar 

  14. Bruni, V., Piccoli, B., Vitulano, D.: A fast computation method for time scale signal denoising. Signal Image Video Process. 3(1), 63–83 (2009)

    Article  MATH  Google Scholar 

  15. Daubechies, I.: Ten lectures on wavelets. In: CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 61, 2nd edn. SIAM, Philadelphia (1992)

  16. Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press, New York (1998)

    MATH  Google Scholar 

  17. Donoho, D.L., Johstone, I.M.: Adapting to unknown smoothness via wavelet shrinkage. J. Am. Stat. Assoc. 90(432), 1200–1224 (1995)

    Article  MATH  Google Scholar 

  18. Tomasi, C., Manduchi R.: Bilateral filtering for gray and color images. In: Proceedings of 6th International Conference Computer Vision, Bombay, pp. 839–846 (1998)

  19. Smith, S.M., Brady, J.M.: Susan—a new approach to low level image processing. Int. J. Comput. Vis. 23(1), 45–78 (1997)

    Article  Google Scholar 

  20. Yaroslavsky, L.: Digital Picture Processing—An Introduction. Springer, Berlin (1985)

    Book  MATH  Google Scholar 

  21. Barash, D.: A fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation. In: IEEE Trans PAMI 24(6), 844–847 (2002)

    Article  Google Scholar 

  22. Elad, M.: On the origin of the bilateral filter and ways to improve it. In: IEEE Trans Image Process. 11(10), 1141–1151 (2002)

    Article  MathSciNet  Google Scholar 

  23. Morillas, S., Gregori, V., Sapena, A.: Fuzzy bilateral filtering for color images. Lecture Notes in Computer Science, pp. 138–145 (2006)

  24. Overton, K.J., Weymouth, T.E.: A noise reducing preprocessing algorithm. IEEE Proceedings of Computer Science Conference Pattern Recognition and Image Process, Chicago, pp. 498–507 (1979)

  25. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. In: IEEE Trans PAMI. 12(7), 629–639 (1990)

    Article  Google Scholar 

  26. Zhang, B., Allebach, J.P.: Adaptive bilateral filter for sharpness enhancement and noise removal. In: IEEE Trans. Image Process. 17(5), 664–678 (2008)

    Article  MathSciNet  Google Scholar 

  27. Eisemann, E., Durand, F.: Flash photography enhancement via intrinsic relighting. In: Proceedings of the SIGGRAPH Conference. ACM Transactions on Graphics, 23(3), pp. 673–678 (2004)

  28. Zhang, M., Gunturk, B.K.: Multiresolution bilateral filtering for image denoising. In: IEEE Trans Image Process. 17(12), 2324–2333 (2008)

    Article  MathSciNet  Google Scholar 

  29. Wenxuan, S., Jie, L., Minyuan, W.: An image denoising method based on multiscale wavelet thresholding and bilateral filtering. Wuhan Univ. J. Nat. Sci. 15(2), 148–152 (2010)

    Article  MathSciNet  Google Scholar 

  30. Mustafa, Z.A., Kadah, Y.M.: Multi resolution bilateral filter for MR image denoising. In: Proceedings of 1st Middle East Conference on Biomedical Engineering (MECBME), Sharjah, pp. 180–184 (2011)

  31. Roy, S., Sinha, N., Sen, A.K.: A new hybrid image denoising method. Int. J. Inf. Technol. Knowl. Manag. 2(2), 491–497 (2010)

    Google Scholar 

  32. Shreyamsha Kumar, B.K.: Image denoising based on gaussian/bilateral filter and its method noise thresholding. J. SIViP (2012). doi:10.1007/s11760-012-0372-7

  33. Buades, A., Coll, B., Morel, J.: Neighborhood filters and pde’s. Numerische Mathematik 105, 1–34 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  34. Kervrann, C., Boulanger, J.: Optimal spatial adaptation for patch-based image denoising. In: IEEE Trans. Image Process. 15(10), 2866–2878 (2006)

    Article  Google Scholar 

  35. Xu, H., Xu, J., Wu, F.: On the biased estimation of nonlocal means filter. In: International Conference on Multimedia and Expo (ICME), Hannover, pp. 1149–1152 (2008)

  36. Buades, A., Coll, B., Morel, J.M.: A review of image denoising methods, with a new one. Multiscale Model. Simul. 4(2), 490–530 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  37. Stein, C.: Estimation of the mean of a multivariate normal distribution. Ann. Stat. 9(6), 1135–1151 (1981)

    Article  MATH  Google Scholar 

  38. Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3D transform-domain collaborative filtering. In: IEEE Trans. Image Process. 16(8), 2080–2095 (2007)

    Article  MathSciNet  Google Scholar 

  39. Shivamurti, M., Narasimhan, S.V.: Analytic discrete cosine harmonic wavelet transform (ADCHWT) and its application to signal/image denoising. In: International Conference on Signal Processing and Communications (SPCOM), Bangalore, pp. 1–5 (2010). doi:10.1109/SPCOM.2010.5560554

  40. Shreyamsha Kumar, B.K.: Image Denoising Using Discrete Cosine Harmonic Wavelets. Technical Report, Sensor Signal Process. Group, Central Research Lab. Bharat Electronics, Bangalore (2010)

  41. Shreyamsha Kumar, B.K.: Multifocus and multispectral image fusion based on pixel significance using discrete cosine harmonic wavelet transform. J. SIViP (2012). doi:10.1007/s11760-012-0361-x

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Acknowledgments

The author would like to express his gratitude to Mr. C. R. Patil, Member (Senior Research Staff), CRL-BEL, India, for his helpful and constructive comments. Also, the author would like to thank Dr. A. T. Khalghatgi, Director (R & D), BEL, India, for his constant encouragement and support to carry out this work.

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Authors and Affiliations

  1. Central Research Laboratory, Bharat Electronics, Bangalore, 560013, India

    B. K. Shreyamsha Kumar

  2. Department of Electrical and Computer Engineering, Concordia University, 1515 St.Catherine West, Montreal, QC, H3G 2W1, Canada

    B. K. Shreyamsha Kumar

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Correspondence to B. K. Shreyamsha Kumar.

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Shreyamsha Kumar, B.K. Image denoising based on non-local means filter and its method noise thresholding. SIViP 7, 1211–1227 (2013). https://doi.org/10.1007/s11760-012-0389-y

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