Skip to main content
SpringerLink
Log in

Variational mode decomposition based image denoising using semi-adaptive conductance function inspired diffusion filtering

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

In day-to-day life, images are the most frequent and casual way of information sharing. These images are susceptible to external disturbances or noise. Thus, to curb noise, image denoising algorithms are utilized. In this paper, the variational mode decomposition, with its concurrent and a non-recursive process for determining the mode functions that also provides a robust method for image denoising, has been introduced. This decomposition process divides the whole spectrum of the signal into a number of sub-bands or mode functions, centered around their respective center frequencies. To these mode functions, spatial filters such as bilateral filter, wiener filter, and modified anisotropic diffusion filter are employed. These filters help in enhancing the yield of the quality assessment metrics; such as mean square error (MSE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM), together with the semi-adaptive conductance function in the diffusion filter. The parameters of these respective spatial filters are calibrated, and then selected in order to get the best possible metric scores. The applicability and ability of the algorithm to suppress noise are compared visually and quantitatively for the noisy image using modified variational mode decomposition and other denoising algorithms in both low and high noise levels. The algorithm provides an average decrease of 62% in case of MSE, 28% increase in PSNR, and 110% increase in SSIM when compared with other denoising techniques. The estimated metric score values signify that the proposed method has a better prospect as a denoising algorithm.

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
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data availability

All the data required for this research work are available publicly and can be accessed from the Hlevkin database website (http://www.hlevkin.com/hlevkin/06testimages.htm), and LIDC-IDRI database of the Cancer Imaging Archive (https://wiki.cancerimagingarchive.net/pages/viewpage.action?pageId=1966254).

References

  1. Armato SG, McLennan G, Bidaut L et al (2011) The Lung Image Database Consortium (LIDC) and Image Database Resource Initiative (IDRI): A completed reference database of lung nodules on CT scans. Med Phys 38:915–931. https://doi.org/10.1118/1.3528204

    Article  Google Scholar 

  2. Ben HA, Krim H (2001) Image denoising: A nonlinear robust statistical approach. IEEE Trans Signal Process 49:3045–3054. https://doi.org/10.1109/78.969512

    Article  Google Scholar 

  3. Dragomiretskiy K, Zosso D (2014) Variational mode decomposition. IEEE Trans Signal Process 62:531–544. https://doi.org/10.1109/TSP.2013.2288675

    Article  MathSciNet  Google Scholar 

  4. Efford N (2000) Digital Image Processing: A Practical Introduction Using Java. Addison-Wesley Longman Publishing Co., Inc.

    Google Scholar 

  5. Egiazarian KO, Astola JT, Helsingius MP, Kuosmanen P (1999) Adaptive denoising and lossy compression of images in transform domain. J Electr Imag 8:233–245

    Article  Google Scholar 

  6. Eskicioglu AM, Fisher PS (1993) A Survey of Quality Measures for Gray scale Image Compression. Proc 1993 Sp earth Sci data compression Work Utah, 1993 49–61. https://doi.org/10.2514/6.1993-4514

  7. Florencio DAF, Schafer RW (1994) Decision-based median filter using local signal statistics. In: Proc.SPIE

  8. Gilboa G, Sochen N, Zeevi YY (2006) Estimation of optimal PDE-based denoising in the SNR sense. IEEE Trans Image Proc 15:2269–2280. https://doi.org/10.1109/TIP.2006.875248

    Article  Google Scholar 

  9. Gonzalez RC, Woods RE (2002) Digital Image Processing, 2nd edn. Prentice-Hall, Upper Saddle River, NJ

    Google Scholar 

  10. Gupta H, Singh H, Kumar A, Vishwakarma A (2022) Adaptive conductance function based improved diffusion filtering and bi-dimensional empirical mode decomposition based image denoising. Multidimens Syst Signal Process 1–45. https://doi.org/10.1007/S11045-022-00850-Y/FIGURES/26

  11. Han D, Yuan X (2012) A Note on the Alternating Direction Method of Multipliers. J Optim Theory Appl 155:227–238. https://doi.org/10.1007/s10957-012-0003-z

    Article  MathSciNet  Google Scholar 

  12. Healey G, Kondepudy R (1992) CCD camera calibration and noise estimation. Proc IEEE Comput Soc Conf Comput Vis Pattern Recognit 1992-June:90–95. https://doi.org/10.1109/CVPR.1992.223222

  13. Hlevkin Database (n.d.) http://www.hlevkin.com/hlevkin/06testimages.htm

  14. Huang NE, Shen Z, Long SR et al (1998) The empirical mode decomposition and the Hubert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc A Math Phys Eng Sci 454:903–995. https://doi.org/10.1098/rspa.1998.0193

    Article  Google Scholar 

  15. Ibrahim H, Kong NSP, Ng TF (2008) Simple adaptive median filter for the removal of impulse noise from highly corrupted images. IEEE Trans Consum Electron 54:1920–1927. https://doi.org/10.1109/TCE.2008.4711254

    Article  Google Scholar 

  16. Kommuri SVR, Singh H, Kumar A, Bajaj V (2020) Bidimensional Empirical Mode Decomposition-Based Diffusion Filtering for Image Denoising. Circuits, Syst Signal Proc 39:5127–5147. https://doi.org/10.1007/s00034-020-01404-y

    Article  Google Scholar 

  17. Kumar M, Bhandari AK, Singh N, Ghosh A (2021) A new multilevel histogram thresholding approach using variational mode decomposition. Multimed Tools Appl 80:11331–11363. https://doi.org/10.1007/s11042-020-10189-w

    Article  Google Scholar 

  18. Lian J, Liu Z, Wang H, Dong X (2018) Adaptive variational mode decomposition method for signal processing based on mode characteristic. Mech Syst Signal Process 107:53–77. https://doi.org/10.1016/j.ymssp.2018.01.019

    Article  Google Scholar 

  19. Liu K, Xu W, Wu H, Yahya AA (2023) Weighted hybrid order total variation model using structure tensor for image denoising. Multimed Tools Appl 82:927–943. https://doi.org/10.1007/s11042-022-12393-2

    Article  Google Scholar 

  20. Luo W (2006) Efficient removal of impulse noise from digital images. IEEE Trans Consum Electron 52:523–527. https://doi.org/10.1109/TCE.2006.1649674

    Article  Google Scholar 

  21. Mafi M, Martin H, Cabrerizo M et al (2019) A comprehensive survey on impulse and Gaussian denoising filters for digital images. Signal Process 157:236–260. https://doi.org/10.1016/j.sigpro.2018.12.006

    Article  Google Scholar 

  22. Mohanty S, Gupta KK, Raju KS (2015) Comparative study between VMD and EMD in bearing fault diagnosis. 9th Int Conf Ind Inf Syst ICIIS 2014. https://doi.org/10.1109/ICIINFS.2014.7036515

  23. Nguyen P, Kang M, Kim JM et al (2015) Robust condition monitoring of rolling element bearings using de-noising and envelope analysis with signal decomposition techniques. Expert Syst Appl 42:9024–9032. https://doi.org/10.1016/J.ESWA.2015.07.064

    Article  Google Scholar 

  24. Pathak M, Sinha GR (2014) A Survey Of Fuzzy Based Image Denoising Techniques. IOSR J Electron Commun Eng 9:27–36

    Article  Google Scholar 

  25. Perona P, Malik J (1990) Scale-Space and Edge Detection Using Anisotropic Diffusion. IEEE Trans Pattern Anal Mach Intell 12:629–639. https://doi.org/10.1109/34.56205

    Article  Google Scholar 

  26. Regularization D, Chan RH, Ho C, Nikolova M Salt-and-Pepper Noise Removal by Median-type Noise Detectors. Compute 1–14

  27. Singh I, Neeru N (2014) Performance Comparison of Various Image Denoising Filters under Spatial Domain. Int J Comput Appl 96:21–30. https://doi.org/10.5120/16903-6969

    Article  Google Scholar 

  28. Singh H, Kommuri SVR, Kumar A, Bajaj V (2021) A new technique for guided filter based image denoising using modified cuckoo search optimization. Expert Syst Appl 176:114884. https://doi.org/10.1016/J.ESWA.2021.114884

    Article  Google Scholar 

  29. Singh H, Kumar A, Balyan LK, Lee HN (2021) Spatial Entropy Quartiles-Based Texture-Aware Fractional-Order Unsharp Masking for Visibility Enhancement of Remotely Sensed Images. IEEE Trans Syst Man, Cybern Syst https://doi.org/10.1109/TSMC.2021.3049402

  30. Singh H, Kumar A, Balyan LK (2023) Fractional-order Differintegral based multiscale Retinex inspired texture dependent quality enhancement for remotely sensed images. Multimed Tools Appl 82:1593–1631. https://doi.org/10.1007/S11042-022-13265-5/TABLES/12

    Article  Google Scholar 

  31. Srinivasan KS, Ebenezer D (2007) A new fast and efficient decision-based algorithm for removal of high-density impulse noises. IEEE Signal Process Lett 14:189–192. https://doi.org/10.1109/LSP.2006.884018

    Article  Google Scholar 

  32. Toh VKK, Isa NAM (2010) Noise Adaptive Fuzzy Switching Median Filter for Salt-and-Pepper Noise Reduction 17:281–284

  33. Toh KKV, Ibrahim H, Mahyuddin MN (2008) Salt-and-pepper noise detection and reduction using fuzzy switching median filter. IEEE Trans Consum Electron 54:1956–1961. https://doi.org/10.1109/TCE.2008.4711258

    Article  Google Scholar 

  34. Tomasi C, Manduchi R (1998) Bilateral filtering for gray and color images. Proc IEEE Int Conf Comput Vis 839–846. https://doi.org/10.1109/iccv.1998.710815

  35. Tsiotsios C, Petrou M (2013) On the choice of the parameters for anisotropic diffusion in image processing. Pattern Recogn 46:1369–1381. https://doi.org/10.1016/j.patcog.2012.11.012

    Article  Google Scholar 

  36. Varma DR (2012) Managing DICOM images: Tips and tricks for the radiologist. Indian J Radiol Imaging 22:4–13. https://doi.org/10.4103/0971-3026.95396

    Article  Google Scholar 

  37. Vasanth K, Jawahar Senthil Kumar V (2015) Decision-based neighborhood-referred unsymmetrical trimmed variants filter for the removal of high-density salt-and-pepper noise in images and videos. Signal, Image Video Proc 9:1833–1841. https://doi.org/10.1007/s11760-014-0665-0

    Article  Google Scholar 

  38. Veerakumar T, Subudhi BN, Esakkirajan S (2019) Empirical mode decomposition and adaptive bilateral filter approach for impulse noise removal. Expert Syst Appl 121:18–27. https://doi.org/10.1016/J.ESWA.2018.12.009

    Article  Google Scholar 

  39. Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: From error visibility to structural similarity. IEEE Trans Image Process 13:600–612. https://doi.org/10.1109/TIP.2003.819861

    Article  Google Scholar 

  40. Xu J, Jia Y, Shi Z, Pang K (2016) An improved anisotropic diffusion filter with semi-adaptive threshold for edge preservation. Signal Process 119:80–91. https://doi.org/10.1016/j.sigpro.2015.07.017

    Article  Google Scholar 

  41. Xue YJ, Cao JX, Wang DX et al (2016) Application of the Variational-Mode Decomposition for Seismic Time-frequency Analysis. IEEE J Sel Top Appl Earth Obs Remote Sens 9:3821–3831. https://doi.org/10.1109/JSTARS.2016.2529702

    Article  Google Scholar 

  42. Zhang P, Li F (2014) A new adaptive weighted mean filter for removing salt-and-pepper noise. IEEE Signal Process Lett 21:1280–1283. https://doi.org/10.1109/LSP.2014.2333012

    Article  Google Scholar 

Download references

Funding

There is no financing organization for the supporting distribution.

Author information

Authors and Affiliations

  1. Department of Electronics and Communication Engineering, Indian Institute of Information Technology, Design and Manufacturing, Jabalpur, 482005, India

    Himanshu Gupta, Anil Kumar & Amit Vishwakarma

  2. Department of Electronics and Communication Engineering, National Institute of Technology Karnataka, Surathkal, Karnataka, 575025, India

    Himanshu Singh

  3. Department of Electrical Engineering, Indian Institute Technology Roorkee, Uttrakhand, 247667, India

    Girish Kumar Singh

Authors
  1. Himanshu Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Himanshu Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anil Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Amit Vishwakarma
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Girish Kumar Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Himanshu Gupta.

Ethics declarations

Conflict of Interest

No conflict of interest.

Additional information

Publisher’s note

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

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

Gupta, H., Singh, H., Kumar, A. et al. Variational mode decomposition based image denoising using semi-adaptive conductance function inspired diffusion filtering. Multimed Tools Appl 83, 7433–7456 (2024). https://doi.org/10.1007/s11042-023-15863-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-023-15863-3

Keywords

Search

Navigation