Automatic, Fast and Robust Characterization of Noise Distributions for Diffusion MRI

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11070)


Knowledge of the noise distribution in magnitude diffusion MRI images is the centerpiece to quantify uncertainties arising from the acquisition process. The use of parallel imaging methods, the number of receiver coils and imaging filters applied by the scanner, amongst other factors, dictate the resulting signal distribution. Accurate estimation beyond textbook Rician or noncentral chi distributions often requires information about the acquisition process (e.g.coils sensitivity maps or reconstruction coefficients), which is not usually available. We introduce a new method where a change of variable naturally gives rise to a particular form of the gamma distribution for background signals. The first moments and maximum likelihood estimators of this gamma distribution explicitly depend on the number of coils, making it possible to estimate all unknown parameters using only the magnitude data. A rejection step is used to make the method automatic and robust to artifacts. Experiments on synthetic datasets show that the proposed method can reliably estimate both the degrees of freedom and the standard deviation. The worst case errors range from below 2% (spatially uniform noise) to approximately 10% (spatially variable noise). Repeated acquisitions of in vivo datasets show that the estimated parameters are stable and have lower variances than compared methods.


  1. 1.
    Brown, R.W., et al.: Magnetic resonance imaging: physical principles and sequence design. Wiley, New York (2014)CrossRefGoogle Scholar
  2. 2.
    Dietrich, O., et al.: Influence of multichannel combination, parallel imaging and other reconstruction techniques on MRI noise characteristics. Magn. Reson. Imaging 26(6), 754–762 (2008)CrossRefGoogle Scholar
  3. 3.
    Sotiropoulos, S.N., et al.: Effects of image reconstruction on fiber orientation mapping from multichannel diffusion MRI: reducing the noise floor using SENSE. Magn. Reson. Med. 70(6), 1682–1689 (2013)CrossRefGoogle Scholar
  4. 4.
    Aja-Fernández, S., Vegas-Sánchez-Ferrero, G., Tristán-Vega, A.: Noise estimation in parallel MRI: GRAPPA and SENSE. Magn. Reson. Imaging 32(3), 281–290 (2014)CrossRefGoogle Scholar
  5. 5.
    Collier, Q., et al.: Diffusion kurtosis imaging with free water elimination: a Bayesian estimation approach. Magn. Reson. Med. 80(2), 802–813 (2018)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Sakaie, K., Lowe, M.: Retrospective correction of bias in diffusion tensor imaging arising from coil combination mode. Mag. Reson. Imaging 37, 203–208 (2017)CrossRefGoogle Scholar
  7. 7.
    Veraart, J., Fieremans, E., Novikov, D.S.: Diffusion MRI noise mapping using random matrix theory. Magn. Reson. Med. 76(5), 1582–1593 (2016)CrossRefGoogle Scholar
  8. 8.
    Koay, C.G., Özarslan, E., Pierpaoli, C.: Probabilistic identification and estimation of noise (PIESNO): a self-consistent approach and its applications in MRI. J. Magn. Reson. 199(1), 94–103 (2009)CrossRefGoogle Scholar
  9. 9.
    Tabelow, K., Voss, H.U., Polzehl, J.: Local estimation of the noise level in MRI using structural adaptation. Med. Image Anal. 20(1), 76–86 (2015)CrossRefGoogle Scholar
  10. 10.
    Thom, H.C.S.: A note on the gamma distribution. Mon. Weather Rev. 86(4), 117–122 (1958)CrossRefGoogle Scholar
  11. 11.
    Mirzaalian, H., et al.: Inter-site and inter-scanner diffusion MRI data harmonization. NeuroImage 135, 311–323 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Center for Image SciencesUniversity Medical Center UtrechtUtrechtThe Netherlands

Personalised recommendations