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

TL;DR

This paper introduces an exact method for characterizing noise in 3D-GRAPPA MRI reconstructions by analyzing k-space data directly, leveraging symmetries to manage computational complexity.

Contribution

The novel contribution is an exact k-space analysis method for noise characterization in 3D-GRAPPA MRI, accounting for correlations and symmetries to improve accuracy and feasibility.

Findings

The method provides exact noise estimates under stationarity assumptions.

Simulations and experiments validate the theoretical analysis.

The approach assesses the impact of sampling patterns on noise behavior.

Abstract

Purpose: To characterize the noise distributions in 3D-MRI accelerated acquisitions reconstructed with GRAPPA using an exact noise propagation analysis that operates directly in k--space. Theory and Methods: We exploit the extensive symmetries and separability in the reconstruction steps to account for the correlation between all the acquired k-space samples. Monte Carlo simulations and multi-repetition phantom experiments were conducted to test both the accuracy and feasibility of the proposed method; an in-vivo experiment was performed to assess the applicability of our method to clinical scenarios. Results: Our theoretical derivation shows that the direct k-space analysis renders an exact noise characterization under the assumptions of stationarity and uncorrelation in the original k-space. Simulations and phantom experiments provide empirical support to the theoretical proof. Finally, the in-vivo experiment demonstrates the ability of the proposed method to assess the impact of the sub-sampling pattern on the overall noise behavior. Conclusions: By operating directly in the k-space, the proposed method is able to provide an exact characterization of noise for any Cartesian pattern sub-sampled along the two phase-encoding directions. Exploitation of the symmetries and separability into independent blocks through the image reconstruction procedure allows us to overcome the computational challenges related to the very large size of the covariance matrices involved.