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

Abstract

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 ( urn:x-wiley:07403194:media:mrm26508:mrm26508-math-0004% versus urn:x-wiley:07403194:media:mrm26508:mrm26508-math-0005% in the ascending aorta, urn:x-wiley:07403194:media:mrm26508:mrm26508-math-0006% versus urn:x-wiley:07403194:media:mrm26508:mrm26508-math-0007% 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. Magn Reson Med 78:1330–1341, 2017. © 2016 International Society for Magnetic Resonance in Medicine.