Statistical Noise Models for MRI
Many image-processing applications within MRI are grounded on stochastic methods based on the prior knowledge on the statistics of noise. In this chapter, the noise models for the different acquisitions modalities reviewed in Chap. 2 are presented. The noise in MRI has been traditionally modeled as a stationary process governed by a Rician distribution with constant noise power at each voxel. Modern MRI systems turn this model questionable, making it necessary to develop into more complex patterns. We aim at comprehensively reviewing the main statistical rationales and formulations for the noise in MRI lately found in the literature. The starting point is the complex Gaussian model for the signal acquired in each coil. From there, the different processing and reconstruction schemes are analyzed to generate the models of noise on the final composite magnitude signals. Gaussian, Rician, and noncentral-\(\chi \) distributions will be considered, as well as stationary and non-stationary models. Finally, we explore the applicability of the surveyed models to some MRI protocols commonly used. Whereas many parallel and nonparallel acquisitions like GRAPPA and SENSE may be fitted into one of the existing models, other nonlinear reconstruction procedures are lacking a proper noise characterization. The chapter is complemented with some practical examples using synthetic and real data.