Noise Filtering in MRI
This chapter is devoted to the problem of noise filtering in MRI from a signal estimation perspective. Noise filtering can be found in the literature under very different denominations: noise filtering, noise removal, denoising, noise reduction and signal estimation. Here, we analyze and categorize the different approaches and evaluate their goodness for specific purposes: the selection of a method must be based on the precise needs of the problem in hand. There is no all-purpose filter that could perform excellent in all situations with the same configuration of parameters. To that end, first, we establish the basic requirements to use a filtering scheme in medical imaging in general and in MRI in particular. Then, we review the different uses that filtering can have and we show some examples of the advantage of carry out a noise reduction procedure on MRI. Later, we analyze the different approaches in the literature and evaluate their performance for specific purposes. As a case study, we examine the different modifications provided in literature over a well-known filter, the LMMSE estimator for Rician noise, in order to better cope with different modalities of MRI.