Iterative Off-resonance and Signal Decay Correction for Improved Multi-echo Imaging in MRI

Local deviations of the main field and signal decay due to transverse relaxation lead to perturbations of the Fourier encoding commonly applied in magnetic resonance imaging. Hence, images acquired with trajectories having long readout times suffer from artefacts such as blurring, geometric distortion, and intensity inhomogeneity. These effects can be corrected by means of iterative reconstruction algorithms, provided a field map and a relaxation map are available. Recently, a fast griddingbased approach to field inhomogeneity correction was proposed. In this work, this algorithm is extended to also handle the signal decay due to relaxation. It is then embedded in a novel fixedpoint iteration algorithm that allows for the joint estimation of the field map, relaxation map, and echo images from a single multi-echo acquisition. This joint estimation approach enables the application of fast acquisition trajectories in multi-echo imaging experiments, such as spiral and echo planar, while avoiding artefacts in the reconstruction of the echo images, the field map, and the relaxation map. Since the method dispenses with the acquisition of a separate calibration scan, an appreciable overall reduction in scan time can be achieved. The evaluation of the proposed algorithm in simulations and in-vivo experiments shows a significant improvement in the reconstruction of the echo images and the estimation of the relaxation map, as compared to the standard case, where no correction is applied. The demonstrated rapid convergence of the fixed-point iteration algorithm together with the computational efficiency of the gridding-based reconstruction keeps the overall computation time reasonable.