[Paper Review] Multi-shot multi-channel diffusion data recovery using structured low-rank matrix completion

Merry Mani, Mathews Jacob+2 more|arXiv (Cornell University)|Feb 22, 2016

Advanced Neuroimaging Techniques and Applications41 references3 citations

TL;DR

This paper proposes MUSSELS, a calibration-less method for reconstructing multi-shot diffusion-weighted MRI data by exploiting structured low-rank matrix completion to implicitly compensate for motion-induced phase variations without explicit phase estimation. The method lifts k-space data into a block-Hankel matrix structure, leverages null-space vectors from smooth phase modulations to enforce low-rank structure, and uses nuclear-norm minimization with data consistency to recover unaliased images, achieving superior ghosting artifact reduction compared to conventional SENSE and phase-based methods, especially under under-sampling or noisy conditions.

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 the unaliased images. In the new formulation, the k-space data of the unaliased 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 fully-sampled as well as under-sampled MS-DW data. Results: Our experiments on in-vivo data show effective removal of the ghosting artifacts arising from intershot motion in MS-DW data using the proposed method. The performance is comparable and better in certain cases than conventional phase-based methods. Conclusion: The proposed method can achieve effective unaliasing of fully/under-sampled MS-DW images without using explicit phase estimates.

Motivation & Objective

• To address ghosting artifacts in multi-shot diffusion-weighted imaging (MS-DWI) caused by inter-shot motion-induced phase variations.
• To eliminate the need for explicit estimation of motion-induced phase maps, which are error-prone in under-sampled or noisy data.
• To develop a robust, calibration-less reconstruction method that enables effective unaliasing of fully-sampled and under-sampled MS-DWI data.
• To improve image quality and tensor estimation accuracy in DTI by reducing residual aliasing from motion artifacts.

Proposed method

• The method constructs a block-Hankel matrix from multi-shot k-space data by applying a sliding window to the k-space data matrix, forming a structured low-rank matrix.
• It exploits the fact that smooth phase modulations between shots create null-space vectors in the structured matrix, implying low-rank structure.
• The unaliased k-space data is recovered via nuclear-norm minimization subject to data consistency constraints, enabling implicit motion compensation.
• The approach incorporates smoothness regularization (SR) to enhance reconstruction quality, particularly in under-sampled or noisy scenarios.
• A joint matrix lifting formulation is used to incorporate partial derivative information in k-space, improving the low-rank approximation of the structured matrix.
• An augmented Lagrangian algorithm is employed to solve the optimization problem, ensuring convergence and stability in the recovery process.

Experimental results

Research questions

• RQ1 Can ghosting artifacts in multi-shot diffusion-weighted imaging be effectively reduced without explicitly estimating motion-induced phase maps?
• RQ2 Can structured low-rank matrix completion provide a robust alternative to phase-based reconstruction in under-sampled or noisy MS-DWI data?
• RQ3 How does the proposed method perform in comparison to conventional SENSE and phase-estimation-based methods like MUSE in terms of artifact reduction and image quality?
• RQ4 To what extent does incorporating smoothness regularization improve the reconstruction of unaliased DWI data?
• RQ5 Can the method achieve reliable unaliasing in high-resolution or ultra-high-field MRI where T2 decay and echo-train length are problematic?

Key findings

• The proposed MUSSELS method successfully removes ghosting artifacts in multi-shot DWI without requiring explicit phase estimation, achieving performance comparable or superior to conventional SENSE and phase-based methods.
• In fully sampled 8-shot data, MUSSELS without smoothness regularization (SR) outperformed TV-MUSE and achieved better fractional anisotropy (FA) maps than both MUSE and SENSE.
• When smoothness regularization was applied, SR-MUSSELS further improved image quality, producing the most accurate FA maps among all methods tested.
• For 4-shot under-sampled data, both uniform and non-uniform sampling patterns showed that MUSSELS achieved effective unaliasing, with unregularized reconstructions performing reasonably well.
• In cases where MUSE failed due to noisy phase estimates, MUSSELS maintained robust performance, demonstrating the advantage of implicit motion compensation over explicit phase estimation.
• The method demonstrated effective recovery of unaliased DWI even in high-field 7T imaging, where long echo times cause significant signal dropout and geometric distortion.