Noise Estimation in Multiple–Coil MR Data

Abstract

The estimators presented in the previous chapter were focused on single-coil acquisitions. Here, we extend those results to the particular case of multiple-coil acquisitions in which the magnitude signal is reconstructed using Sum of Squares (SoS) or a Spatial matched filter (SMF). In addition, we assume that there exist no correlations among coils, and all of them show the same variance of noise. As a consequence, the magnitude signal follows a stationary noncentral- $\chi$ distribution (nc-$\chi$) if SoS is used, or a stationary Rician one, in the case of SMF. We focus on the SoS case and the nc-$\chi$ distribution, since the Rician case is studied in Chap. 7. The main noise estimators for the nc-$\chi$ are thus reviewed and classified. Most of the methods proposed are basically extrapolations of the Rician estimators to the nc-$\chi$. In the last part of the chapter, different estimators are compared and a performance analysis is done using synthetic and real data.