Skip to main content
SpringerLink
Log in

Image denoising by linear regression on non-local means algorithm

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

Non-local means (NL-Means) algorithm which removes the noise from the image have been used in the field widely due to its good performance especially for magnetic resonance images which consists of three dimensional data. Its main idea is using all the pixels which are local and non-local in an image and taking weighted averaging of all values. One negative side of this method is that it considers all pixels in the image without looking at their similarity. This paper proposes an NL-Means algorithm with pixel selection by applying linear regression analysis using root mean squared error (RMSE) value. After regression analysis, RMSE of the neighborhoods is used to exclude non-similar pixels during the noise removal. Lastly, obtained results were compared by four different methods which are NL-Means algorithm and, Gaussian, anisotropic diffusion and median filterings. All of the methods were outperformed by our method on structured similarity index and peak signal-to-noise ratio quantitative metrics. Moreover, the level of increase on visual qualities are also represented as a qualitative analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Availability of data and materials

Not applicable.

Code availability

Source code of the algorithm is available at https://github.com/TugayDirek/Image-Denoising-Using-Pixel-Selection-by-RMSE-with-Non-Local-Means-Algorithm.

References

  1. Alvarez, L., Lions, P.-L., Morel, J.-M.: Image selective smoothing and edge detection by nonlinear diffusion. ii. SIAM J. Numer. Anal. 29(3), 845–866 (1992). https://doi.org/10.1137/0729052

    Article  MathSciNet  Google Scholar 

  2. Coifman, R.R., Donoho, D.L.: Translation-invariant de-noising, 125–150 (1995) https://doi.org/10.1007/978-1-4612-2544-7_9

  3. Donoho, D.L.: De-noising by soft-thresholding. IEEE Trans. Inf. Theory 41(3), 613–627 (1995). https://doi.org/10.1109/18.382009

    Article  MathSciNet  Google Scholar 

  4. Lindenbaum, M., Fischer, M., Bruckstein, A.: On Gabor’s contribution to image enhancement. Pattern Recogn. 27(1), 1–8 (1994). https://doi.org/10.1016/0031-3203(94)90013-2

    Article  ADS  Google Scholar 

  5. Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60(1), 259–268 (1992). https://doi.org/10.1016/0167-2789(92)90242-F

    Article  MathSciNet  ADS  Google Scholar 

  6. Smith Stephen M., B.J.M.: a new approach to low level image processing (1997/05/01)

  7. Gupta, M.D., Xiao, J.: Bi-affinity filter: a bilateral type filter for color images, 27–40 (2012)

  8. Yaroslavsky, L.P.: Introduction, 1–5 (1985). https://doi.org/10.1007/978-3-642-81929-2_1

  9. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990). https://doi.org/10.1109/34.56205

    Article  Google Scholar 

  10. Linwei, F., Fan, Z., Hui, F., Caiming, Z.: Brief review of image denoising techniques. In: Visual Computing for Industry, Biomedicine, and Art (2019). https://doi.org/10.1186/s42492-019-0016-7

  11. Lim, J.S.: Two-dimensional signal and image processing. In: Visual Computing for Industry, Biomedicine, and Art (1990)

  12. Goyal, B., Dogra, A., Agrawal, S., Sohi, B.S., Sharma, A.: Image denoising review: From classical to state-of-the-art approaches. Inf. Fusion 55, 220–244 (2020). https://doi.org/10.1016/j.inffus.2019.09.003

    Article  Google Scholar 

  13. Zhang, K., Zuo, W., Chen, Y., Meng, D., Zhang, L.: Beyond a gaussian denoiser: residual learning of deep cnn for image denoising. IEEE Trans. Image Process. 26(7), 3142–3155 (2017). https://doi.org/10.1109/TIP.2017.2662206

    Article  MathSciNet  PubMed  ADS  Google Scholar 

  14. Buades, A., Coll, B., Morel, J.-M.: Non-local means denoising. Image Process. On Line 1, 208–212 (2011). https://doi.org/10.5201/ipol.2011.bcm_nlm

    Article  Google Scholar 

  15. Liu, Y.L., Wang, J., Chen, X.: A robust and fast non-local means algorithm for image denoising. J. Comput. Sci. Technol. (2008). https://doi.org/10.1007/s11390-008-9129-8

    Article  MathSciNet  Google Scholar 

  16. Bonar, D., Sacchi, M.: Denoising seismic data using the nonlocal means algorithm. Geophysics 77(1), 5–8 (2012) https://doi.org/10.1190/geo2011-0235.1, https://arxiv.org/abs/https://pubs.geoscienceworld.org/geophysics/article-pdf/77/1/A5/3225089/geo2011-0235.pdf

  17. Zhang, H., Zeng, D., Zhang, H., Wang, J., Liang, Z., Ma, J.: Applications of nonlocal means algorithm in low-dose x-ray ct image processing and reconstruction: A review. Medical Physics 44(3), 1168–1185 (2017) https://doi.org/10.1002/mp.12097, https://arxiv.org/abs/https://aapm.onlinelibrary.wiley.com/doi/pdf/10.1002/mp.12097

  18. Wu, K., Zhang, X., Ding, M.: Curvelet based nonlocal means algorithm for image denoising. AEU-Int. J. Electron. C. 68(1), 37–43 (2014). https://doi.org/10.1016/j.aeue.2013.07.011

    Article  Google Scholar 

  19. Lu, S., Ouyang, S., Xiao, L.: Mri denoising using pixel-selection-based non-local means, 1412–1417 (2016) https://doi.org/10.1109/CISP-BMEI.2016.7852938

  20. Bazdaric, K., Sverko, D., Salaric, I., Martinovic, A., Lucijanic, M.: The abc of linear regression analysis: What every author and editor should know 47 (2021) https://doi.org/10.3897/ese.2021.e63780

  21. Díaz, A., Steele, D.: Analysis of the robustness of NMF algorithms. CoRR abs/2106.02213 (2021) arXiv:2106.02213

  22. Horé, A., Ziou, D.: Image quality metrics: Psnr vs. ssim. In: 2010 20th International Conference on Pattern Recognition, pp. 2366–2369 (2010). https://doi.org/10.1109/ICPR.2010.579

  23. Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004). https://doi.org/10.1109/TIP.2003.819861

    Article  PubMed  ADS  Google Scholar 

Download references

Acknowledgements

I would like to thank Assoc. Prof. Pınar Oğuz Ekim for her contributions. I also would like to thank to reviewers for their detailed comments on the article.

Funding

Not applicable.

Author information

Authors and Affiliations

  1. Software Engineering, Izmir University of Economics, Sakarya Street, Izmir, Turkey

    Tugay Direk

Authors
  1. Tugay Direk
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

T. D. implemented and wrote all parts of the study.

Corresponding author

Correspondence to Tugay Direk.

Ethics declarations

Conflict of interest

There is no conflict of interest issue.

Ethics approval

Not applicable.

Consent to participate

Not applicable.

Consent for publication

Not applicable.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix A: Comparison of different methods

Appendix A: Comparison of different methods

See Figs. 6, 7 and 8.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Direk, T. Image denoising by linear regression on non-local means algorithm. SIViP (2024). https://doi.org/10.1007/s11760-024-03086-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11760-024-03086-4

Keywords

Search

Navigation