iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://doi.org/10.1007/s11760-024-03280-4
Fourth-order partial differential diffusion model with adaptive Laplacian kernel for low-dose CT image processing | Signal, Image and Video Processing Skip to main content
Log in

Fourth-order partial differential diffusion model with adaptive Laplacian kernel for low-dose CT image processing

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

Abstract

Low-dose computed tomography (LDCT) reduces radiation damage to patients, however, it adds noise and artifacts to the reconstructed images, which deteriorates the quality of CT images. To address the problem of easy edge blurring in the denoising process of LDCT images, this paper proposes a fourth-order partial differential diffusion model with adaptive Laplacian kernel that can protect edge and detail information. The model incorporates the guided filter with edge preserving as a fidelity term in the energy function. Then, using gradient magnitude and the local variance to construct edge and detail detectors in the diffusion function, which can protect the edge and detail information of the LDCT images during the diffusion process. Finally, using the adaptive Laplacian kernel replaces the conventional Laplacian kernel, which has stronger edge preserving. The experimental results show that the proposed model achieves excellent performance in edge preserving and noise suppression in actual thoracic phantom and AAPM clinical LDCT images. In terms of both visual effects and quantitative indexes, the proposed model has good processing performance compared with other excellent algorithms.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Data availability

The source code and the images used in this paper have been uploaded to GitHub at https://github.com/LeiWang-learning/ALFOD.

References

  1. Hart, D., Wall, B.F.: UK population dose from medical X-ray examinations. Eur. J. Radiol. 50, 285–291 (2004). https://doi.org/10.1016/S0720-048X(03)00178-5

    Article  Google Scholar 

  2. Slovis, T.L.: Children, computed tomography radiation dose, and the as low as reasonably achievable (ALARA) concept. Pediatrics 112(4), 971–972 (2003). https://doi.org/10.1542/peds.112.4.971

    Article  Google Scholar 

  3. Limin, L., Yining, H., Yang, C.: Research status and prospect for low-dose CT image. J. Data Acquis. Proc. 30, 24–34 (2015). https://doi.org/10.16337/j.1004-9037.2015.01.002

    Article  Google Scholar 

  4. Balda, M., Hornegger, J., Heismann, B.: Ray contribution masks for structure adaptive sinogram filtering. IEEE Trans. Med. Imaging 30(5), 1116–1128 (2011). https://doi.org/10.1109/TMI.2012.2187213

    Article  Google Scholar 

  5. Zhang, Y., Wang, Y., Zhang, W., Lin, F., Pu, Y., Zhou, J.: Statistical iterative reconstruction using adaptive fractional order regularization. Biomed. Opt. Express 7(3), 1015–1029 (2016). https://doi.org/10.1364/BOE.7.001015

    Article  Google Scholar 

  6. Mohd Sagheer, S.V., George, S.N.: Denoising of low-dose CT images via low-rank tensor modeling and total variation regularization. Artif. Intell. Med. 94, 1–17 (2019). https://doi.org/10.1016/j.artmed.2018.12.006

    Article  Google Scholar 

  7. Chen, W., Shao, Y., Wang, Y., et al.: A novel total variation model for low-dose CT image denoising. IEEE Access 6(1), 78892–78903 (2018). https://doi.org/10.1109/ACCESS.2018.2885514

    Article  Google Scholar 

  8. Feruglio, P.F., Vinegoni, C., Gros, J., Sbarbati, A., Weissleder, R.: Block matching 3D random noise filtering for absorption optical projection tomography. Phys. Med. Biol. 55(18), 5401–5415 (2010). https://doi.org/10.1088/0031-9155/55/18/009

    Article  Google Scholar 

  9. Kang, J., Gui, Z., Liu, Y., et al.: LDCT image quality improvement algorithm based on optimal wavelet basis and MCA. SIViP 16, 2303–2311 (2022). https://doi.org/10.1007/s11760-022-02196-1

    Article  Google Scholar 

  10. Trung, N.T., Trinh, D.H., Trung, N.L., et al.: Low-dose CT image denoising using deep convolutional neural networks with extended receptive fields. SIViP 16, 1963–1971 (2022). https://doi.org/10.1007/s11760-022-02157-8

    Article  Google Scholar 

  11. Kang, E., Chang, W., Yoo, J., Ye, J.C.: Deep convolutional framelet denosing for low-dose CT via wavelet residual network. IEEE Trans. Med. Imaging 37(6), 1358–1369 (2018). https://doi.org/10.1109/TMI.2018.2823756

    Article  Google Scholar 

  12. The 2016 NIH-AAPM-Mayo Clinic Low Dose CT Grand Challenge. Accessed: Jan. 18, 2016. [Online]. Available: http://www.aapm.org/GrandChallenge/LowDoseCT.

  13. 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 

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

    Article  MathSciNet  Google Scholar 

  15. Wang, Y.Q., Guo, J., Chen, W., Zhang, W.: Image denoising using modified Perona-Malik model based on directional Laplacian. Signal Process. 93(9), 2548–2558 (2013). https://doi.org/10.1016/j.sigpro.2013.02.020

    Article  Google Scholar 

  16. Lu, W., Duan, J., Qiu, Z., Pan, Z., Liu, R.W., Bai, L.: Implementation of high-order variational models made easy for image processing. Math. Method. Appl. Sci. 39(14), 4208–4233 (2016). https://doi.org/10.1002/mma.3858

    Article  MathSciNet  Google Scholar 

  17. Duan, J., Qiu, Z., Lu, W., Wang, G., Pan, Z., Bai, L.: An edge-weighted second order variational model for image decomposition. Digit. Signal Proc. 49, 162–181 (2016). https://doi.org/10.1016/j.dsp.2015.10.010

    Article  Google Scholar 

  18. You, Y.L., Kaveh, M.: Fourth-order partial differential equations for noise removal. IEEE Trans. Image Process. 9(10), 1723–1730 (2000). https://doi.org/10.1109/83.869184]

    Article  MathSciNet  Google Scholar 

  19. Hajiaboli, M.R.: An anisotropic fourth-order diffusion filter for image noise removal. Int. J. Comput. Vis. 92, 177–191 (2011). https://doi.org/10.1007/s11263-010-0330-1

    Article  MathSciNet  Google Scholar 

  20. Lysaker, M., Lundervold, A., Tai, X.-C.: Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE Trans. Image Proc. 12(12), 1579–1590 (2003). https://doi.org/10.1109/TIP.2003.819229

    Article  Google Scholar 

  21. Liu, Y., Chen, Y., Chen, P., Qiao, Z., Gui, Z.: Artifact suppressed nonlinear diffusion filtering for low-dose CT image processing. IEEE Access. 7, 109856–109869 (2019). https://doi.org/10.1109/ACCESS.2019.2933541

    Article  Google Scholar 

  22. Hajiaboli, M.R.: A self-governing fourth-order nonlinear diffusion filter for image noise removal. IPSJ Trans. Comput. Vis. Appl. 2, 94–103 (2010). https://doi.org/10.2197/ipsjtcva.2.94

    Article  Google Scholar 

  23. He, K., Sun, J., Tang, X.: Guided image filtering. IEEE Trans. Pattern anal. Mach. Intell. 35(6), 1397–1409 (2012). https://doi.org/10.1109/TPAMI.2012.213

    Article  Google Scholar 

  24. Chao, S.M., Tsai, D.M.: An improved anisotropic diffusion model for detail- and edge-preserving smoothing. Pattern Recognit. Lett. 31(13), 2012–2023 (2010). https://doi.org/10.1016/j.patrec.2010.06.004

    Article  Google Scholar 

  25. Rafsanjani, H.K., Sedaaghi, M.H., Saryazdi, S.: An adaptive diffusion coefficient selection for image denoising. Digit. Signal Process. 64, 71–82 (2017). https://doi.org/10.1016/j.dsp.2017.02.004

    Article  MathSciNet  Google Scholar 

  26. Tebini, S., Seddik, H., Braiek, E.B.: An advanced and adaptive mathematical function for an efficient anisotropic image filtering. Comput. Math. Appl. 72(5), 1369–1385 (2016). https://doi.org/10.1016/j.camwa.2016.07.004]

    Article  MathSciNet  Google Scholar 

  27. Hajiaboli, M.R., Ahmad, M.O., Wang, C.: An edge-adapting laplacian kernel for nonlinear diffusion filters. IEEE Trans. Image Process. 21(4), 1561–1572 (2012). https://doi.org/10.1109/TIP.2011.2172803

    Article  MathSciNet  Google Scholar 

  28. Alvarez, L., Mazorra, L.: Signal and image restoration using shock filters and anisotropic diffusion. SIAM J. Numer. Anal. 31(2), 590–605 (1994). https://doi.org/10.1137/0731032

    Article  MathSciNet  Google Scholar 

  29. Fu, S.J., Zhang, C.M., Tai, X.C.: Image denoising and deblurring: non-convex regularization, inverse diffusion and shock filter. SCIENCE CHINA Inf. Sci. 54, 1184–1198 (2011). https://doi.org/10.1007/s11432-011-4239-2

    Article  MathSciNet  Google Scholar 

  30. Chen, Y., Dai, X., Duan, H., Gao, L., Sun, X., Nie, S.: A quality improvement method for lung LDCT images. J. Xray Sci. Technol. 28(2), 255–270 (2020). https://doi.org/10.3233/XST-190605

    Article  Google Scholar 

  31. 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  Google Scholar 

  32. Zhang, L., Zhang, L., Mou, X., Zhang, D.: FSIM: a feature similarity index for image quality assessment. IEEE Trans. Image Process. 20(8), 2378–2386 (2011). https://doi.org/10.1109/TIP.2011.2109730

    Article  MathSciNet  Google Scholar 

  33. Xue, W., Zhang, L., Mou, X., Bovik, A.C.: Gradient magnitude similarity deviation: a highly efficient perceptual image quality index. IEEE Trans. Image Process. 23(2), 684–695 (2014). https://doi.org/10.1109/TIP.2013.2293423

    Article  MathSciNet  Google Scholar 

  34. Canny, J.: A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8(6), 679–698 (1986). https://doi.org/10.1109/TPAMI.1986.4767851]

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Nature Science Foundation of China under Grant (61801438), the Science and Technology Innovation Project of Colleges and Universities of Shanxi Province under Grant (2020L0282), the Natural Science Foundation of Shanxi Province under Grant (202103021224204).

Author information

Authors and Affiliations

Authors

Contributions

Lei Wang, Yi Liu, and Zhiguo Gui wrote the main manuscript text, Rui Wu, RongbiaoYan, Yuhang Liu prepared figures and tables. Shilei Ren and Yan Chen participated in the discussion and provided some advice. All authors reviewed the manuscript.

Corresponding author

Correspondence to Zhiguo Gui.

Ethics declarations

Conflict of interest

The authors declare no conflicts 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

Wang, L., Liu, Y., Wu, R. et al. Fourth-order partial differential diffusion model with adaptive Laplacian kernel for low-dose CT image processing. SIViP 18, 5907–5917 (2024). https://doi.org/10.1007/s11760-024-03280-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-024-03280-4

Keywords

Navigation