Regression models for identifying noise sources in magnetic resonance images

Hongtu Zhu, Yimei Li, Joseph G. Ibrahim, Xiaoyan Shi, Hongyu An, Yashen Chen, Wei Gao, Weili Lin, Daniel B. Rowe, Bradley S. Peterson

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


Stochastic noise, susceptibility artifacts, magnetic field and radiofrequency inhomogeneities, and other noise components in magnetic resonance images (MRIs) can introduce serious bias into any measurements made with those images.We formally introduce three regression models including a Rician regression model and two associated normal models to characterize stochastic noise in various magnetic resonance imaging modalities, including diffusion-weighted imaging (DWI) and functional MRI (fMRI). Estimation algorithms are introduced to maximize the likelihood function of the three regression models.We also develop a diagnostic procedure for systematically exploring MR images to identify noise components other than simple stochastic noise, and to detect discrepancies between the fitted regression models and MRI data. The diagnostic procedure includes goodness-of-fit statistics, measures of influence, and tools for graphical display. The goodnessoffit statistics can assess the key assumptions of the three regression models, whereas measures of influence can isolate outliers caused by certain noise components, including motion artifacts. The tools for graphical display permit graphical visualization of the values for the goodness-of-fit statistic and influence measures. Finally, we conduct simulation studies to evaluate performance of these methods, and we analyze a real dataset to illustrate how our diagnostic procedure localizes subtle image artifacts by detecting intravoxel variability that is not captured by the regression models.

Original languageEnglish
Pages (from-to)623-637
Number of pages15
JournalJournal of the American Statistical Association
Issue number486
StatePublished - Jun 2009


  • Diffusion tensor
  • Goodness-of-fit statistic
  • Influence measures
  • Normal approximation
  • Rician regression
  • Visualization


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