Parametric Noise Analysis from Correlated Multiple-Coil MR Data

Abstract

Nonaccelerated multiple-coil acquisitions have extensively used non-central-\(\chi \) (nc-\(\chi \)) statistics as a substitute for the traditional Rician model. However, this model is only valid when the signals received by each coil are uncorrelated, the variance of noise in each coil is the same and the reconstruction is done using the sum of squares (SoS) approach. The recent literature on this topic suggests that this is often not the case, so that nc-\(\chi \) statistics are in principle not adequate. We consider two cases for the magnitude signal being constructed using either a SMF or a SoS approach. In the former case, a non-stationary Rician distribution arises, with a single parameter \(\sigma ^{2}(\mathbf{x})\). In the latter, an nc- \(\chi \) approximation of the data is considered, namely an effective noise power (greater than the actual power of thermal noise in the RF receiver) and an effective number of coils (smaller than the actual number of RF receiving coils in the system). In both cases, the distributions turn non-stationary and the parameters of noise in the magnitude image become position dependent: instead of a single value, a noise map \(\sigma ^{2}(\mathbf{x})\) must be estimated instead. In this chapter, we will focus on a parametric estimation of the noise parameters: the estimation is done considering the process that has generated the specific model of noise with the knowledge of some extra parameters. We propose some estimation guidelines for this specific problem under the restrictions posed by the model.