Computation of exact g-factor maps in 3D GRAPPA reconstructions.

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; a high-resolution 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 high-resolution 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.

Joint groupwise registration and ADC estimation in the liver using a B-value weighted metric.

PURPOSE: The purpose of this work is to develop a groupwise elastic multimodal registration algorithm for robust ADC estimation in the liver on multiple breath hold diffusion weighted images. METHODS: We introduce a joint formulation to simultaneously solve both the registration and the estimation problems. In order to avoid non-reliable transformations and undesirable noise amplification, we have included appropriate smoothness constraints for both problems. Our metric incorporates the ADC estimation residuals, which are inversely weighted according to the signal content in each diffusion weighted image. RESULTS: Results show that the joint formulation provides a statistically significant improvement in the accuracy of the ADC estimates. Reproducibility has also been measured on real data in terms of the distribution of ADC differences obtained from different b-values subsets. CONCLUSIONS: The proposed algorithm is able to effectively deal with both the presence of motion and the geometric distortions, increasing accuracy and reproducibility in diffusion parameters estimation.