A New Nonlocal Maximum Likelihood Estimation Method for Denoising Magnetic Resonance Images

  • Jeny Rajan
  • Arnold J. den Dekker
  • Jaber Juntu
  • Jan Sijbers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8251)


Denoising of Magnetic Resonance images is important for proper visual analysis, accurate parameter estimation, and for further preprocessing of these images. Maximum Likelihood (ML) estimation methods were proved to be very effective in denoising Magnetic Resonance (MR) images. Among the ML based methods, the recently proposed Non Local Maximum Likelihood (NLML) approach gained much attention. In the NLML method, the samples for the ML estimation of the true underlying intensity are selected in a non local way based on the intensity similarity of the pixel neighborhoods. This similarity is generally measured using the Euclidean distance. A drawback of this approach is the usage of a fixed sample size for the ML estimation and, as a result, optimal results cannot be achieved because of over- or under-smoothing. In this work, we propose an NLML estimation method for denoising MR images in which the samples are selected in an adaptive way using the Kolmogorov-Smirnov (KS) similarity test. The method has been tested both on simulated and real data, showing its effectiveness.


Image denoising Kolmogorov-Smirnov test MRI Noise Rice distribution 


  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. Imag. Proc. 17, 1383–1398 (2008)CrossRefGoogle Scholar
  2. 2.
    Aja-Fernández, S., Tristán, A., Alberola-López, C.: Noise estimation in single and multiple coil magnetic resonance data based on statistical models. Magn. Reson. Imaging 27, 1397–1409 (2009)CrossRefGoogle Scholar
  3. 3.
    Bhattacharyaa, A.: On the measure of divergence between two statistical populations defined by their probability distributions. Bull. Calcutta Math. Soc. 35, 99–109 (1943)MathSciNetGoogle Scholar
  4. 4.
    Cocosco, C.A., Kollokian, V., Kwan, R.-S., Evans, A.C.: Brainweb: Online interface to a 3D MRI simulated brain database. NeuroImage 5(4), S425 (1997),
  5. 5.
    Gerig, G., Kubler, O., Kikinis, R., Jolesz, F.A.: Nonlinear anisotropic filtering of MRI data. IEEE Trans. Med. Imag. 11(2), 221–232 (1992)CrossRefGoogle Scholar
  6. 6.
    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
  7. 7.
    Manjón, J.V., Carbonell-Caballero, J., Lull, J.J., García-Martí, G., Martí-Bonmatí, L., Robles, M.: MRI denoising using non local means. Medical Image Analysis 12, 514–523 (2008)CrossRefGoogle Scholar
  8. 8.
    Manjón, J.V., Coupé, P., Martí-Bonmatíand, L., Collins, D.L., Robles, M.: Adaptive non local means denoising of MR images with spatially varying noise levels. J. Magn. Reson. Imaging 31, 192–203 (2010)CrossRefGoogle Scholar
  9. 9.
    Rajan, J., Jeurissen, B., Verhoye, M., Van Audekerke, J., Sijbers, J.: Maximum likelihood estimation-based denoising of magnetic resonance images using restricted local neighborhoods. Physics in Medicine and Biology 56, 5221–5234 (2011)CrossRefGoogle Scholar
  10. 10.
    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)Google Scholar
  11. 11.
    Rajan, J., Poot, D., Juntu, J., Sijbers, J.: Segmentation based noise variance estimation from background mri data. In: Campilho, A., Kamel, M. (eds.) ICIAR 2010, Part I. LNCS, vol. 6111, pp. 62–70. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Rice, S.O.: Mathematical analysis of random noise. Bell. Syst. Tech. 23, 282–332 (1944)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Sijbers, J., den Dekker, A.J.: Maximum likelihood estimation of signal amplitude and noise variance from MR data. Magn. Reson. Med. 51(3), 586–594 (2004)CrossRefGoogle Scholar
  14. 14.
    Sijbers, J., den Dekker, A.J., Scheunders, P., Van Dyck, D.: Maximum likelihood estimation of Rician distribution parameters. IEEE Trans. Med. Imag. 17(3), 357–361 (1998)CrossRefGoogle Scholar
  15. 15.
    Sijbers, J., den Dekker, A.J., Verhoye, M., Van Audekerke, J., Van Dyck, D.: Estimation of noise from magnitude MR images. Magn. Reson. Imaging 16(1), 87–90 (1998)CrossRefGoogle Scholar
  16. 16.
    Sijbers, J., Poot, D., den Dekker, A.J., Pintjens, W.: Automatic estimation of the noise variance from the histogram of a magnetic resonance image. Phys. Med. Biol. 52, 1335–1348 (2007)CrossRefGoogle Scholar
  17. 17.
    Wang, Z., Bovik, A., Sheik, H.R., Simoncelli, E.P.: Image quality assessment: From error visibility to structural similarity. IEEE Trans. on Image Pocessing 13, 600–612 (2004)CrossRefGoogle Scholar
  18. 18.
    Wink, A.M., Roerdink, B.T.M.: BOLD noise assumptions in fMRI. International Journal of Biomedical Imaging 2006, 1–11 (2006)CrossRefGoogle Scholar
  19. 19.
    Zimmer, S., Didas, S., Weickert, J.: A rotationally invariant block matching strategy improving image denoising with non-local means. In: International Workshop on Local and Non-Local Approximation in Image Processing, Switzerland, pp. 135–142 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jeny Rajan
    • 1
    • 2
  • Arnold J. den Dekker
    • 3
  • Jaber Juntu
    • 2
  • Jan Sijbers
    • 2
  1. 1.Department of Computer Science and EngineeringNational Institute of Technology - KarnatakaSurathkalIndia
  2. 2.iMinds Vision Lab, Department of PhysicsUniversity of AntwerpBelgium
  3. 3.Delft Center for Systems and ControlDelft University of TechnologyDelftThe Netherlands

Personalised recommendations