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

Abstract

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.

Ghost reduction in echo‐planar imaging by joint reconstruction of images and line‐to‐line delays and phase errors

“…It may however be useful as a preprocessing step to correct even/odd delays and phase shifts within each shot individually, which would then be followed by higher order inter-shot phase correction using a method such as Ref. [25]. It may also be possible to estimate higher order phase error maps using EPI-TrACR by increasing its polynomial order, or to estimate a spatially resolved phase error map for each shot and set of even or odd lines; the latter approach would likely require spatial regularization of the estimated phase error maps [34].…”

“…Importantly, with the exception of the multi-shot diffusion EPI phase-corrected reconstruction method of Ref. [25], most of these calibration-free retrospective methods are either incompatible or have not been validated with multi-shot EPI, and are either incompatible with parallel imaging acceleration or have only been validated with small acceleration factors of 2× or less. At the same time, to our knowledge the method of Ref.…”

“…At the same time, to our knowledge the method of Ref. [25] has not been applied to correct even/odd phase shifts and delays within each shot, but instead relied on calibration data for those corrections.…”

A General Framework for Compressed Sensing and Parallel MRI Using Annihilating Filter Based Low-Rank Hankel Matrix

“…The first one is wavelet-based pyramidal decomposition approach and the second one is a generalization for multichannel parallel MRI. Note that these are particular instances of the ALOHA algorithm and other variations of ALOHA may be possible for various scenarios as demonstrated in recent applications [32]- [34].…”

A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery

“…Inspired by auto-calibration techniques in parallel MRI [12]–[15], the extension to recovery of parallel MRI from undersampled measurements is formulated as a structured low-rank matrix recovery problem in [2], [10]. Similar approaches have also been found very effective in auto-calibrated multishot MRI [16] and correction of echo-planar MRI data [17]. The theoretical performance of structured low-rank matrix completion methods has been studied in [3], [18], [19], showing improved statistical performance over standard discrete spatial domain recovery.…”