Statistical Noise Model in GRAPPA-Reconstructed Images

Santiago Aja-Fernandez¹, Antonio Tristan-Vega¹, Scott Hoge²

A statistical noise model is derived for multiple-coil MR signals when using subsampling and GRAPPA reconstruction methods. The reconstructed data in each coil is shown to follow a non-stationary Gaussian distribution. Under some assumptions the signal may be considered as nearly stationary. For each pixel, if the coefficient of variation of the noise variance across coils is low enough, a non-central Chi model may be considered. This is the same model used for non-subsampled multiple-coil acquisitions. However, the non-central Chi model is not always assured in GRAPPA reconstructed data.