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Multi‐shot sensitivity‐encoded diffusion data recovery using structured low‐rank matrix completion (MUSSELS)
Author(s) -
Mani Merry,
Jacob Mathews,
Kelley Douglas,
Magnotta Vincent
Publication year - 2017
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.26382
Subject(s) - matrix completion , computer science , matrix norm , algorithm , artifact (error) , low rank approximation , matrix (chemical analysis) , regularization (linguistics) , missing data , artificial intelligence , computer vision , mathematics , physics , gaussian , mathematical analysis , quantum mechanics , hankel matrix , eigenvalues and eigenvectors , materials science , machine learning , composite material
Purpose To introduce a novel method for the recovery of multi‐shot diffusion weighted (MS‐DW) images from echo‐planar imaging (EPI) acquisitions. Methods Current EPI‐based MS‐DW reconstruction methods rely on the explicit estimation of the motion‐induced phase maps to recover artifact‐free images. In the new formulation, the k‐space data of the artifact‐free DWI is recovered using a structured low‐rank matrix completion scheme, which does not require explicit estimation of the phase maps. The structured matrix is obtained as the lifting of the multi‐shot data. The smooth phase‐modulations between shots manifest as null‐space vectors of this matrix, which implies that the structured matrix is low‐rank. The missing entries of the structured matrix are filled in using a nuclear‐norm minimization algorithm subject to the data‐consistency. The formulation enables the natural introduction of smoothness regularization, thus enabling implicit motion‐compensated recovery of the MS‐DW data. Results Our experiments on in‐vivo data show effective removal of artifacts arising from inter‐shot motion using the proposed method. The method is shown to achieve better reconstruction than the conventional phase‐based methods. Conclusion We demonstrate the utility of the proposed method to effectively recover artifact‐free images from Cartesian fully/under‐sampled and partial Fourier acquired data without the use of explicit phase estimates. Magn Reson Med 78:494–507, 2017. © 2016 International Society for Magnetic Resonance in Medicine