This unique text presents a comprehensive review of methods for modeling signal and noise in magnetic resonance imaging (MRI), providing a systematic study, classifying and comparing the numerous and varied estimation and filtering techniques. Features: provides a complete framework for the modeling and analysis of noise in MRI, considering different modalities and acquisition techniques; describes noise and signal estimation for MRI from a statistical signal processing perspective; surveys the different methods to remove noise in MRI acquisitions from a practical point of view; reviews different techniques for estimating noise from MRI data in single- and multiple-coil systems for fully sampled acquisitions; examines the issue of noise estimation when accelerated acquisitions are considered, and parallel imaging methods are used to reconstruct the signal; includes appendices covering probability density functions, combinations of random variables used to derive estimators, and useful MRI datasets.