Skip to main content

Advertisement

SpringerLink
Log in

Brain fiber structure estimation based on principal component analysis and RINLM filter

  • Original Article
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

Diffusion magnetic resonance imaging is a technique for non-invasive detection of microstructure in the white matter of the human brain, which is widely used in neuroscience research of the brain. However, diffusion-weighted images(DWI) are sensitive to noise, which affects the subsequent reconstruction of fiber orientation direction, microstructural parameter estimation and fiber tracking. In order to better eliminate the noise in diffusion-weighted images, this study proposes a noise reduction method combining Marchenko-Pastur principal component analysis(MPPCA) and rotation-invariant non-local means filter(RINLM) to further remove residual noise and preserve the image texture detail information. In this study, the algorithm is applied to the fiber structure and the prevailing microstructural models within the human brain voxels based on simulated and real human brain datasets. Experimental comparisons between the proposed method and the state-of-the-art methods are performed in single-fiber, multi-fiber, crossed and curved-fiber regions as well as in different microstructure estimation models. Results demonstrated the superior performance of the proposed method in denoising DWI data, which can reduce the angular error in fiber orientation reconstruction to obtain more valid fiber structure estimation and enable more complete fiber tracking trajectories with higher coverage. Meanwhile, the method reduces the estimation errors of various white matter microstructural parameters and verifies the performance of the method in white matter microstructure estimation.

Graphical abstract

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
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Basser PJ, Mattiello J, Lebihan D (1994) MR diffusion tensor spectroscopy and imaging. Biophys J 66(1):259–267

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  2. Soares JM, Ricardo M, Moreira PS et al (2016) A Hitchhiker’s guide to functional magnetic resonance imaging. Front Neurosci 10:515

    Article  PubMed  PubMed Central  Google Scholar 

  3. Jeurissen B, Descoteaux M, Mori S et al (2019) Diffusion MRI fiber tractography of the brain. NMR Biomed 32(4):e3785

    Article  PubMed  Google Scholar 

  4. Tournier JD, Calamante F, Connelly A (2013) Determination of the appropriate b value and number of gradient directions for high angular resolution diffusion weighted imaging. NMR Biomed 26(12):1775–1786

    Article  PubMed  Google Scholar 

  5. Tuch DS, Reese TG, Wiegell MR et al (2002) High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. Magn Reson Med 48(4):577–582

    Article  PubMed  Google Scholar 

  6. Tournier JD, Calamante F, Connelly A (2007) Robust determination of the fibre orientation distribution in diffusion MRI: non-negativity constrained super-resolved spherical deconvolution. Neuroimage 35(4):1459–1472

    Article  PubMed  Google Scholar 

  7. Thanh DNH, Kalavathi P, Prasath VBS (2020) Chest X-ray image denoising using Nesterov optimization method with total variation regularization. Procedia Comput Sci 171:1961–1969

    Article  Google Scholar 

  8. Tavakoli A, Mousavi P, Zarmehi F et al (2018) Modified algorithms for image inpainting in Fourier transform domain. Comput Appl Math 37(4):5239–5252

    Article  MathSciNet  Google Scholar 

  9. Lu W, Duan J, Qiu Z et al (2016) Implementation of high-order variational models made easy for image processing. Math Methods Appl Sci 39(14):4208–4233

    Article  MathSciNet  Google Scholar 

  10. Tian C, Zheng M, Zuo W et al (2023) Multi-stage image denoising with the wavelet transform. Pattern Recogn 134:109050

    Article  Google Scholar 

  11. Göreke V (2023) A novel method based on Wiener filter for denoising Poisson noise from medical X-Ray images. Biomed Signal Process Control 79:104031

    Article  Google Scholar 

  12. Lahmiri S (2017) An iterative denoising system based on Wiener filtering with application to biomedical images. Opt Laser Technol 90:128–132

    Article  ADS  Google Scholar 

  13. Muresan DD, Parks TW (2003) Adaptive principal components and image denoising. IEEE Int Conf Image Process 1:101–104

    Google Scholar 

  14. Zhang L, Dong W, Zhanga D, Shib G (2010) Two-stage image denoising by principal component analysis with local pixel grouping. Pattern Recogn 43(4):1531–1549

    Article  ADS  Google Scholar 

  15. Phophalia A, Mitra SK (2017) 3D MR image denoising using rough set and kernel PCA method. Magn Reson Imaging 36:135–145

    Article  PubMed  Google Scholar 

  16. Veraart J, Novikov DS, Novikov DS et al (2016a) Denoising of diffusion MRI using random matrix theory. Neuroimage 142:394–406

    Article  PubMed  Google Scholar 

  17. Zhang XY, Peng J, Xu M et al (2017) Denoise diffusion-weighted images using higher-order singular value decomposition. Neuroimage 156:128–145

    Article  PubMed  Google Scholar 

  18. Wu ZX, Potter T, Wu DN et al (2018) Denoising high angular resolution diffusion imaging data by combining singular value decomposition and non-local means filter. J Neurosci Methods 312:105–113

    Article  PubMed  Google Scholar 

  19. Veraart J, Fieremans E et al (2016b) Diffusion MRI noise mapping using random matrix theory. Magn Reson Med 76(5):1582–1593

  20. Manjon JV, Coupé P, Concha L et al (2013) Diffusion weighted image denoising using overcomplete local PCA. PLoS ONE 8(9):12

    Article  Google Scholar 

  21. Manjón JV, Coupé P, Buades A (2015) MRI noise estimation and denoising using non-local PCA. Med Image Anal 22(1):35–47

    Article  PubMed  Google Scholar 

  22. Priya US, Nair JJ (2015) Denoising of DT-MR images with an iterative PCA. Procedia Comput Sci 58:603–613

    Article  Google Scholar 

  23. Marchenko VA, Pastur LA (1967) Distribution of eigenvalues for some sets of random matrices. Mat Sb 114:507–536

    Google Scholar 

  24. Moeller S, Pisharady PK, Ramanna S et al (2021) NOise reduction with DIstribution Corrected (NORDIC) PCA in dMRI with complex-valued parameter-free locally low-rank processing. Neuroimage 226:117539

    Article  PubMed  Google Scholar 

  25. Manjón JV, Coupé P, Buades A, Collins DL, Robles M (2012) New methods for MRI denoising based on sparseness and self-similarity. Med Image Anal 16(1):18–27

    Article  PubMed  Google Scholar 

  26. Fadnavis S, Batson J, Garyfallidis E (2020) Patch2Self: denoising diffusion MRI with self-supervised learning. Adv Neural Inf Process Syst 33:16293–16303

    Google Scholar 

  27. Rajan J, Veraart J, Van Audekerke J et al (2012) Nonlocal maximum likelihood estimation method for denoising multiple coil magnetic resonance images. Magn Reson Imaging 30(10):1512–1518

    Article  PubMed  Google Scholar 

  28. Zhang Y, Liu J, Li M et al (2014) Joint image denoising using adaptive principal component analysis and self-similarity. Inform Sci 259:128–141

    Article  Google Scholar 

  29. Zhu H, Zhang J, Wang Z (2018) Arterial spin labeling perfusion MRI signal denoising using robust principal component analysis. Neurosci Meth 295:10–19

    Article  Google Scholar 

  30. Buades A, Coll B, Morel J-M (2005) On image denoising methods. SIAM Multiscale Model Simul 4(2):490–530

    Article  MathSciNet  Google Scholar 

  31. Hansen PC (1994) Regularization tools: a MATLAB package for analysis and solution of discrete ill-posed problems. Numer Algorithms 6:1–35

    Article  ADS  MathSciNet  Google Scholar 

  32. Smith RE, Tournier JD, Calamante F et al (2012) Anatomically-constrained tractography: improved diffusion MRI streamlines tractography through effective use of anatomical information. Neuroimage 62(3):1924–1938

    Article  PubMed  Google Scholar 

  33. Smith SM, Jenkinson M, Woolrich MW et al (2004) Advances in functional and structural MR image analysis and implementation as FSL. Neuroimage 23(Suppl 1):S208–S219

    Article  PubMed  Google Scholar 

  34. Tournier JD, Calamante F, Connelly A (2010) Improved probabilistic streamlines tractography by 2nd order integration over fibre orientation distributions. Proceedings of the international society for magnetic resonance in medicine, 1670

  35. Jensen JH, Helpern JA, Ramani A et al (2005) Diffusional kurtosis imaging: the quantification of non-Gaussian water diffusion by means of magnetic resonance imaging. Magn Reson Med 53(6):1432–1440

    Article  PubMed  Google Scholar 

  36. Zhang H, Schneider T, Wheeler-Kinshott CA et al (2012) NODDI: practical in vivo neurite orientation dispersion and density imaging of the human brain. Neuroimage 61(4):1000–1016

    Article  PubMed  Google Scholar 

  37. Fillard P, Descoteaux M, Goh A et al (2011) Quantitative evaluation of 10 tractography algorithms on a realistic diffusion MR phantom. Neuroimage 56(1):220–234

    Article  PubMed  Google Scholar 

  38. Close TG, Tournier JD, Calamante F et al (2009) A software tool to generate simulated white matter structures for the assessment of fibre-tracking algorithms. Neuroimage 47(4):1288–1300

    Article  PubMed  Google Scholar 

  39. Tournier JD, Smith R, Raffelt D et al (2019) MRtrix3: a fast, flexible and open software framework for medical image processing and visualisation. Neuroimage 202:116137

    Article  PubMed  Google Scholar 

  40. Pizzolato M, Gilbert G, Thiran JP et al (2020) Adaptive phase correction of diffusion-weighted images. Neuroimage 206:116274

    Article  PubMed  Google Scholar 

  41. Liu F, Feng J, Chen G et al (2021) Gaussianization of diffusion MRI data using spatially adaptive filtering. Med Image Anal 68:101828

    Article  PubMed  Google Scholar 

  42. Liu F, Yang J, Feng M et al (2023) Does perfect filtering really guarantee perfect phase correction for diffusion MRI data? Comput Med Imaging Graph 103:102160

    Article  PubMed  Google Scholar 

Download references

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Author information

Authors and Affiliations

  1. Institute of Medical Imaging and Engineering, University of Shanghai for Science and Technology, Shanghai, China

    Yuemin Zhu & Yuanjun Wang

Authors
  1. Yuemin Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuanjun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Zhu Yuemin and Wang Yuanjun. The first draft of the manuscript was written by Zhu Yuemin and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Yuanjun Wang.

Ethics declarations

Ethics approval

Since this paper is based on a publicly available dataset, no ethical statement is required.

Competing interests

The authors have no relevant financial or non-financial interests to disclose.

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

Zhu, Y., Wang, Y. Brain fiber structure estimation based on principal component analysis and RINLM filter. Med Biol Eng Comput 62, 751–771 (2024). https://doi.org/10.1007/s11517-023-02972-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-023-02972-2

Keywords

Search

Navigation