Noise Estimation in Single-Coil MR Data
The different approaches to estimate \(\sigma ^2\) out of Rician magnitude MR images are reviewed and classified, assuming the noise to be stationary, i.e., \(\sigma \) does not depend on the position. Most of the approaches to noise estimation in MRI in the literature are precisely focused on this kind of noise. The different methods are systematized and classified attending their nature. As a case study, a special kind of estimators, those based on the calculation of local moments, is deeply studied. This case serves as an illustration of the different considerations that must be taken into account when implementing an estimation procedure. In the last part of the chapter, the advantages and drawbacks of the different methods are analyzed through synthetic and real data controlled experiments. The estimators for Rician noise of here reviewed are the basis for many of the estimators proposed in the following chapters, which can be seen as extensions of these.