General formulation for quantitative G-factor calculation in GRAPPA reconstructions.

In this work a theoretical description for practical quantitative estimation of the noise enhancement in generalized autocalibrating partially parallel acquisitions (GRAPPA) reconstructions, equivalent to the geometry (g)-factor in sensitivity encoding for fast MRI (SENSE) reconstructions, is described. The GRAPPA g-factor is derived directly from the GRAPPA reconstruction weights. The procedure presented here also allows the calculation of quantitative g-factor maps for both the uncombined and combined accelerated GRAPPA images. This enables, for example, a fast comparison between the performances of various GRAPPA reconstruction kernels or SENSE reconstructions. The applicability of this approach is validated on phantom studies and demonstrated using in vivo images for 1D and 2D parallel imaging.