Signal, Image and Video Processing

, Volume 11, Issue 5, pp 913–920 | Cite as

A nonlocal maximum likelihood estimation method for enhancing magnetic resonance phase maps

  • P. V. Sudeep
  • P. Palanisamy
  • Chandrasekharan Kesavadas
  • Jan Sijbers
  • Arnold J. den Dekker
  • Jeny Rajan
Original Paper


A phase map can be obtained from the real and imaginary components of a complex valued magnetic resonance (MR) image. Many applications, such as MR phase velocity mapping and susceptibility mapping, make use of the information contained in the MR phase maps. Unfortunately, noise in the complex MR signal affects the measurement of parameters related to phase (e.g, the phase velocity). In this paper, we propose a nonlocal maximum likelihood (NLML) estimation method for enhancing phase maps. The proposed method estimates the true underlying phase map from a noisy MR phase map. Experiments on both simulated and real data sets indicate that the proposed NLML method has a better performance in terms of qualitative and quantitative evaluations when compared to state-of-the-art methods.


Denoising Magnetic resonance image Maximum likelihood estimation Noise Phase map 



This work was partially supported by the Research Foundation-Flanders (FWO, Belgium) through project funding G037813N and the TOP BOF project University of Antwerp (TOP BOF project 26824).


  1. 1.
    Aja-Fernández, S., Alberola-López, C., Westin, C.: Noise and signal estimation in magnitude MRI and Rician distributed images: a LMMSE approach. IEEE Trans. Image Process. 17, 1383–1398 (2008)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bioucas-Dias, J., Katkovnik, V., Astola, J., Egiazarian, K.: Absolute phase estimation: adaptive local denoising and global unwrapping. Appl. Opt. 47(29), 5358–5369 (2002)CrossRefGoogle Scholar
  3. 3.
    Bonny, J.M., Renou, J.P., Zanca, M.: Optimal measurement of magnitude and phase from MR data. J. Magn. Reson. Ser. B 113(2), 136–144 (1996)CrossRefGoogle Scholar
  4. 4.
    Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms, with a new one. Multiscale Model. Simul. 4, 490–530 (2005)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Chavez, S., Xiang, Q.S., An, L.: Understanding phase maps in MRI: a new cutline phase unwrapping method. IEEE Trans. Med. Imaging 21(8), 966–977 (2002)CrossRefGoogle Scholar
  6. 6.
    Cruz-EnrÃquez, H., Lorenzo-Ginori, J.: Combined wavelet and nonlinear filtering for MRI phase images. In: Kamel, M., Campilho, A. (eds.) Image Analysis and Recognition, Lecture Notes in Computer Science, vol. 5627, pp 83–92. Springer, Berlin (2009). iSBN: 978-3-642-02610-2Google Scholar
  7. 7.
    den Dekker, A.J., Sijbers, J.: Data distributions in magnetic resonance images: a review. Phys. Med. 30(7), 725–741 (2014)CrossRefGoogle Scholar
  8. 8.
    Fisher, Y.: Pixelized Data. Springer, London (1995)Google Scholar
  9. 9.
    He, L., Greenshields, I.R.: A nonlocal maximum likelihood estimation method for Rician noise reduction in MR images. IEEE Trans. Med. Imaging 28, 165–172 (2009)CrossRefGoogle Scholar
  10. 10.
    Heydari, M., Karami, M.R., Babakhani, A.: A new adaptive coupled diffusion PDE for MRI Rician noise. Signal Image Video Process. 10(7), 1–8 (2016)Google Scholar
  11. 11.
  12. 12.
    Krissian, K., Aja-Fernández, S.: Noise-driven anisotropic diffusion filtering of MRI. IEEE Trans. Image Process. 18(10), 2265–2274 (2009)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Lorenzo-Ginori, J.V., Plataniotis, K.N., Venetsanopoulos, A.N.: Nonlinear filtering for phase image denoising. IEEE Proc. Vis. Image Signal Process. 149(5), 290–296 (2002)CrossRefGoogle Scholar
  14. 14.
    Manjón, J.V., Carbonell-Caballero, J., Lull, J.J., García-Martí, G., Martí-Bonmatí, L., Robles, M.: Mri denoising using non-local means. Med. Image Anal. 12(4), 514–523 (2008)CrossRefGoogle Scholar
  15. 15.
    Mohan, J., Krishnaveni, V., Guo, Y.: A survey on the magnetic resonance image denoising methods. Biomed. Signal Process. Control 9, 56–69 (2014)CrossRefGoogle Scholar
  16. 16.
    Rajan, J., Poot, D., Juntu, J., Sijbers, J.: Noise measurement from magnitude MRI using local estimates of variance and skewness. Phys. Med. Biol. 55, N441–N449 (2010)CrossRefGoogle Scholar
  17. 17.
    Rajan, J., Jeurissen, B., Verhoye, M., Van Audekerke, J., Sijbers, J.: Maximum likelihood estimation-based denoising of magnetic resonance images using restricted local neighborhoods. Phys. Med. Biol. 56, 5221–5234 (2011)CrossRefGoogle Scholar
  18. 18.
    Rajan, J., Van Audekerke, J., Van der Linden, A., Verhoye, M., Sijbers, J.: An adaptive non local maximum likelihood estimation method for denoising magnetic resonance images. In: 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI), pp 1136–1139. IEEE (2012)Google Scholar
  19. 19.
    Rajan, J., Veraart, J., Van Audekerke, J., Verhoye, M., Sijbers, J.: Nonlocal maximum likelihood estimation method for denoising multiple coil magnetic resonance images. Magn. Reson. Imaging 30(10), 1512–1518 (2012b)CrossRefGoogle Scholar
  20. 20.
    Rajan, J., den Dekker, A.J., Sijbers, J.: A new non-local maximum likelihood estimation method for Rician noise reduction in magnetic resonance images using the Kolmogorov–Smirnov test. Signal Proc. 103, 16–23 (2014)Google Scholar
  21. 21.
    Rauscher, A., Barth, M., Reichenbach, J.R., Stollberger, R., Moser, E.: Automated unwrapping of MR phase images applied to BOLD MR venography at 3 Tesla. Magn. Reson. Imaging 18(2), 175–180 (2003)CrossRefGoogle Scholar
  22. 22.
    Rauscher, A., Barth, M., Reichenbach, J.R., Stollberger, R., Moser, E.: Magnetic susceptibility-weighted MR phase imaging of the human brain. J. Neuroradiol. 26(4), 736–742 (2005)Google Scholar
  23. 23.
    Riji, R., Rajan, J., Sijbers, J., Nair, M.S.: Iterative bilateral filter for Rician noise reduction in MR images. Signal Image Video Process. 9(7), 1543–1548 (2015)CrossRefGoogle Scholar
  24. 24.
    Sharif, M., Hussain, A., Jaffar, M.A., Choi, T.S.: Fuzzy-based hybrid filter for Rician noise removal. Signal Image and Video Process. 10(2), 215–224 (2016)CrossRefGoogle Scholar
  25. 25.
    Sijbers, J., den Dekker, A.J., Scheunders, P., Van Dyck, D.: Maximum likelihood estimation of Rician distribution parameters. IEEE Trans. Med. Imaging 17(3), 357–361 (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2016

Authors and Affiliations

  • P. V. Sudeep
    • 1
    • 2
  • P. Palanisamy
    • 1
  • Chandrasekharan Kesavadas
    • 3
  • Jan Sijbers
    • 4
  • Arnold J. den Dekker
    • 4
    • 5
  • Jeny Rajan
    • 6
  1. 1.Department of Electronics and Communication EngineeringNational Institute of Technology - TiruchirappalliTiruchirappalliIndia
  2. 2.Department of Electronics and Communication EngineeringNational Institute of Technology KarnatakaSurathkalIndia
  3. 3.Department of Imaging Sciences and Intervention RadiologySree Chitra Tirunal Institute for Medical Sciences and TechnologyTrivandrumIndia
  4. 4.iMinds Vision Lab, Department of PhysicsUniversity of AntwerpAntwerpBelgium
  5. 5.Delft Center for Systems and ControlDelft University of TechnologyDelftThe Netherlands
  6. 6.Department of Computer Science and EngineeringNational Institute of Technology KarnatakaSurathkalIndia

Personalised recommendations