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Purpose: To characterize the noise distributions in 3D-MRI acceleratedacquisitions reconstructed with GRAPPA using an exact noise propagationanalysis that operates directly in k--space.  Theory and Methods: We exploit the extensive symmetries and separability inthe reconstruction steps to account for the correlation between all theacquired k-space samples. Monte Carlo simulations and multi-repetition phantomexperiments were conducted to test both the accuracy and feasibility of theproposed method; an in-vivo experiment was performed to assess theapplicability of our method to clinical scenarios.  Results: Our theoretical derivation shows that the direct k-space analysisrenders an exact noise characterization under the assumptions of stationarityand uncorrelation in the original k-space. Simulations and phantom experimentsprovide empirical support to the theoretical proof. Finally, the in-vivoexperiment demonstrates the ability of the proposed method to assess the impactof the sub-sampling pattern on the overall noise behavior.  Conclusions: By operating directly in the k-space, the proposed method isable to provide an exact characterization of noise for any Cartesian patternsub-sampled along the two phase-encoding directions. Exploitation of thesymmetries and separability into independent blocks through the imagereconstruction procedure allows us to overcome the computational challengesrelated to the very large size of the covariance matrices involved.

Computation of Exact g-Factor Maps in 3D GRAPPA Reconstructions