title: Diffusion measurements and diffusion tensor imaging with noisy magnitude data.
abstract: OBJECTIVE
  To compare an unbiased method for estimation of the diffusion coefficient to the quick, but biased, log-linear (LL) method in the presence of noisy magnitude data.
  
  
  METHODS
  The magnitude operation changes the signal distribution in magnetic resonance (MR) images from Gaussian to Rician. If not properly taken into account, this will introduce a bias in the estimated diffusion coefficient. We compare two methods by means of Monte Carlo simulations. The first one applies least-squares fitting of the measured signal to the median (MD) value of the probability density function. The second method is uncorrected LL estimation. We also perform a high-resolution diffusion tensor experiment.
  
  
  RESULTS
  The uncorrected LL estimator is heavily biased at low signal-to-noise ratios. The bias has a significant effect on image quality. The MD estimator is accurate and produces images with excellent contrast.
  
  
  CONCLUSIONS
  In the presence of noisy magnitude data, unbiased estimation is essential in diffusion measurements and diffusion tensor imaging.
authors.affiliation: MR Center, St. Olavs Hospital HF, Trondheim, Norway. anders.kristoffersen@stolav.no
authors.forename: Anders
authors.initials: A
authors.lastname: Kristoffersen
mesh_terms: D000465:Algorithms; D016477:Artifacts; D001921:Brain / Q000033:anatomy & histology*; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity