Accelerating 4D flow MRI by exploiting low-rank matrix structure and hadamard sparsity

Purpose: To develop accelerated 4D flow MRI by exploiting low-rank matrix structure and Hadamard sparsity. Theory and Methods: 4D flow MRI data can be represented as the sum of a low-rank and a sparse component. To optimize the sparse representation of the data, it is proposed to incorporate a Hadamard transform of the velocity-encoding segments. Retrospectively and prospectively, undersampled data of the aorta of healthy subjects are used to assess the reconstruction accuracy of the proposed method relative to k-t SPARSE-SENSE reconstruction. Image reconstruction from eight-fold prospective undersampling is demonstrated and compared with conventional SENSE imaging. Results: Simulation results revealed consistently lower errors in velocity estimation when compared with k-t SPARSE-SENSE. In vivo data yielded reduced error of peak flow with the proposed method relative to k-t SPARSE-SENSE when compared with two-fold SENSE ( 2.5±4.6% versus 10.2±8.5% in the ascending aorta, 3.6±8.4% versus 9.2±9.0% in the descending aorta). Streamline visualization showed more consistent flow fields with the proposed technique relative to the benchmark methods. Conclusion: Image reconstruction by exploiting low-rank structure and Hadamard sparsity of 4D flow MRI data improves the reconstruction accuracy relative to current state-of-the-art methods and holds promise to reduce the long scan times of 4D flow MRI.