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 MR imaging modalities, including diffusion weighted imaging and functional MRI. 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 graphic display. The goodness-of-fit 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 artifact. 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-world dataset to il- lustrate how our diagnostic procedure localizes subtle image artifacts by detecting intravoxel variability that is not captured by the regression models.
Zhu, Hongtu; Li, Yimei ; Ibrahim, Joseph G.; Shi, Xiaoyan; An, Hongyu ; Chen, Yasheng; Lin, Weili; Rowe, Daniel B.; and Peterson, Bradley G., "Regression Models for Identifying Noise Sources in Magnetic Resonance Images" (November 2007). The University of North Carolina at Chapel Hill Department of Biostatistics Technical Report Series. Working Paper 3.