Multi‐shot sensitivity‐encoded diffusion data recovery using structured low‐rank matrix completion (MUSSELS)

• Published in: Magnetic resonance in medicine Vol. 78; no. 2; pp. 494 - 507
• Main Authors: Mani, Merry, Jacob, Mathews, Kelley, Douglas, Magnotta, Vincent
• Format: Journal Article
• Language: English
• Published: United States Wiley Subscription Services, Inc 01.08.2017
• Subjects: Adult; Algorithms; annihilating filter; Brain - diagnostic imaging; calibration‐less; Coding; Data acquisition; Data recovery; Diffusion Magnetic Resonance Imaging - methods; Echo-Planar Imaging; Hoisting; Humans; Image acquisition; Image Processing, Computer-Assisted - methods; Magnetic resonance; Mathematical analysis; Matrix algebra; Matrix methods; Methods; motion compensation; multi‐shot diffusion; Mussels; Reconstruction; Regularization; regularized recovery; Shot; Signal Processing, Computer-Assisted; Smoothness; structured low‐rank; Vectors (mathematics); structured low-rank; multi-shot diffusion; regularized recovery; calibration-less; annihilating filter; motion compensation
• ISSN: 0740-3194; 1522-2594; 1522-2594
• DOI: 10.1002/mrm.26382

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