Statistical Noise Analysis in SENSE Parallel MRI

TL;DR

This paper provides a comprehensive statistical model of noise in SENSE parallel MRI, accounting for coil correlations and reconstruction effects, leading to better understanding of noise behavior and variance across images.

Contribution

It introduces a complete second order statistical characterization of noise in SENSE MRI, extending beyond the first order Rician model to include coil correlations and non-stationarity.

Findings

Noise in SENSE MRI is strongly correlated between adjacent lines.

The noise distribution is non-stationary with varying variance across the image.

Closed-form equations for noise variance and line correlation are derived.

Abstract

A complete first and second order statistical characterization of noise in SENSE reconstructed data is proposed. SENSE acquisitions have usually been modeled as Rician distributed, since the data reconstruction takes place into the spatial domain, where Gaussian noise is assumed. However, this model just holds for the first order statistics and obviates other effects induced by coils correlations and the reconstruction interpolation. Those effects are properly taken into account in this study, in order to fully justify a final SENSE noise model. As a result, some interesting features of the reconstructed image arise: (1) There is a strong correlation between adjacent lines. (2) The resulting distribution is non-stationary and therefore the variance of noise will vary from point to point across the image. Closed equations for the calculation of the variance of noise and the correlation coefficient between lines are proposed. The proposed model is totally compatible with g-factor formulations.