Blind Estimation of Non-stationary Noise in MRI

Abstract

The counterpart of the acceleration capability of parallel MRI (pMRI) techniques, is that the artifact correction techniques affect the nature of noise. As a consequence of the different algorithms, noise in the reconstructed signal becomes non-stationary, i.e., the variance of noise $\sigma ^2(\mathbf{x})$ becomes dependent on the position and, sometimes, also on the signal. Some methods have been proposed in the previous chapters to deal with non-stationary noise in MRI. However, their performance depends on information not usually available, such as multiple acquisitions, the receiver covariance matrix, the sensitivity coil profiles, reconstruction coefficients, or even biophysical models of the data. In this chapter, a different paradigm is considered: blind estimation. The estimation is carried out only assuming a statistical model for the data. No specifics about the transformation, nor extra parameters are needed. The main difficulty of this kind of analysis is that a single value of $\sigma ^2$ no longer characterizes the whole image, on the contrary, a value for each position x must be calculated. We review the different proposals in literature for blind non-stationary noise estimation are reviewed and validated, assuming three different noise models: Gaussian, Rician, and nc-$\chi$. A deeper attention is paid to the homomorphic. Finally, the methods are tested through several synthetic and real data sets.