Maxwell parallel imaging

PURPOSE

To develop a general framework for parallel imaging (PI) with the use of Maxwell regularization for the estimation of the sensitivity maps (SMs) and constrained optimization for the parameter-free image reconstruction.

THEORY AND METHODS

Certain characteristics of both the SMs and the images are routinely used to regularize the otherwise ill-posed optimization-based joint reconstruction from highly accelerated PI data. In this paper, we rely on a fundamental property of SMs-they are solutions of Maxwell equations-we construct the subspace of all possible SM distributions supported in a given field-of-view, and we promote solutions of SMs that belong in this subspace. In addition, we propose a constrained optimization scheme for the image reconstruction, as a second step, once an accurate estimation of the SMs is available. The resulting method, dubbed Maxwell parallel imaging (MPI), works for both 2D and 3D, with Cartesian and radial trajectories, and minimal calibration signals.

RESULTS

The effectiveness of MPI is illustrated for various undersampling schemes, including radial, variable-density Poisson-disc, and Cartesian, and is compared against the state-of-the-art PI methods. Finally, we include some numerical experiments that demonstrate the memory footprint reduction of the constructed Maxwell basis with the help of tensor decomposition, thus allowing the use of MPI for full 3D image reconstructions.

CONCLUSION

The MPI framework provides a physics-inspired optimization method for the accurate and efficient image reconstruction from arbitrary accelerated scans.

On the influence of respiratory motion in radial tissue phase mapping cardiac MRI

PURPOSE

To investigate the impact of respiratory motion on radial tissue phase mapping (TPM) measurements, and to improve image quality and scan efficiency without compromising velocity fidelity by increasing the respiratory acceptance window with and without motion correction.

MATERIALS AND METHODS

A radial golden angle TPM sequence was measured in 10 healthy volunteers in three short axis slices at 3T. Ungated ( CFREE), self-gated with a single acceptance window ( CREF), motion-corrected averaging using all ( CMCall), or selected ( CMC) data reconstructions were compared by means of various image quality measures and resulting velocities.

RESULTS

Using all data ( CFREE) resulted in significantly higher perceived signal-to-noise ratio (SNR) (P < 0.001), but significantly reduced sharpness (P < 0.001) and contrast (P = 0.02), when compared to CREF. Coefficient of variation (CV) and perceived sharpness were not significantly different (P > 0.05). With motion-correction, perceived sharpness could be significantly improved ( CMC: P = 0.002; CMCall: P = 0.002) in comparison to CFREE. Velocity peaks of CFREE were significantly reduced compared to CREF (all peaks: P < 0.001; except the longitudinal "E" peak: P = 0.03). The peak velocities in CMC and CMCall were not significantly different from CREF (all peaks: P > 0.08; except longitudinal "E"/"A" peaks: P > 0.01).

CONCLUSION

Free-breathing reconstruction results in good perceived image sharpness and velocity information with slightly, but significantly, reduced peak velocities. For achieving velocities and image quality comparable to data from a single acceptance window, but higher gating efficiency, selected motion-corrected TPM (CMC) can be applied. J. Magn. Reson. Imaging 2016;44:1218-1228.

Accelerated regularized estimation of MR coil sensitivities using augmented Lagrangian methods

Several magnetic resonance parallel imaging techniques require explicit estimates of the receive coil sensitivity profiles. These estimates must be accurate over both the object and its surrounding regions to avoid generating artifacts in the reconstructed images. Regularized estimation methods that involve minimizing a cost function containing both a data-fit term and a regularization term provide robust sensitivity estimates. However, these methods can be computationally expensive when dealing with large problems. In this paper, we propose an iterative algorithm based on variable splitting and the augmented Lagrangian method that estimates the coil sensitivity profile by minimizing a quadratic cost function. Our method, ADMM-Circ, reformulates the finite differencing matrix in the regularization term to enable exact alternating minimization steps. We also present a faster variant of this algorithm using intermediate updating of the associated Lagrange multipliers. Numerical experiments with simulated and real data sets indicate that our proposed method converges approximately twice as fast as the preconditioned conjugate gradient method over the entire field-of-view. These concepts may accelerate other quadratic optimization problems.