Calibration-Free B0 Correction of EPI Data Using Structured Low Rank Matrix Recovery

Model-based iterative reconstruction for direct imaging with point spread function encoded echo planar MRI

BACKGROUND

Echo planar imaging (EPI) is a fast measurement technique commonly used in magnetic resonance imaging (MRI), but is highly sensitive to measurement non-idealities in reconstruction. Point spread function (PSF)-encoded EPI is a multi-shot strategy which alleviates distortion, but acquisition of encodings suitable for direct distortion-free imaging prolongs scan time. In this work, a model-based iterative reconstruction (MBIR) framework is introduced for direct imaging with PSF-EPI to improve image quality and acceleration potential.

METHODS

An MBIR platform was developed for accelerated PSF-EPI. The reconstruction utilizes a subspace representation, is regularized to promote local low-rankedness (LLR), and uses variable splitting for efficient iteration. Comparisons were made against standard reconstructions from prospectively accelerated PSF-EPI data and with retrospective subsampling. Exploring aggressive partial Fourier acceleration of the PSF-encoding dimension, additional comparisons were made against an extension of Homodyne to direct PSF-EPI in numerical experiments. A neuroradiologists' assessment was completed comparing images reconstructed with MBIR from retrospectively truncated data directly against images obtained with standard reconstructions from non-truncated datasets.

RESULTS

Image quality results were consistently superior for MBIR relative to standard and Homodyne reconstructions. As the MBIR signal model and reconstruction allow for arbitrary sampling of the PSF space, random sampling of the PSF-encoding dimension was also demonstrated, with quantitative assessments indicating best performance achieved through nonuniform PSF sampling combined with partial Fourier. With retrospective subsampling, MBIR reconstructs high-quality images from sub-minute scan datasets. MBIR was shown to be superior in a neuroradiologists' assessment with respect to three of five performance criteria, with equivalence for the remaining two.

CONCLUSIONS

A novel image reconstruction framework is introduced for direct imaging with PSF-EPI, enabling arbitrary PSF space sampling and reconstruction of diagnostic-quality images from highly accelerated PSF-encoded EPI data.

Low rank off-resonance correction for double half-echo k-space acquisitions

The present study describes a model-based approach for correcting off-resonance in the context of double half-echo k-space acquisitions. This technique employs center-out readouts in forward and reverse directions to reduce echo-times but is sensitive to off-resonance, which manifests as pixel shifts in both directions. Demodulating the k-space signal with a constant off-resonance term per slice removes pixel shifts and results in a marked reduction in blurring. Phantom and in vivo datasets are demonstrated from low bandwidth sodium imaging.

MULTI-ECHO RECOVERY WITH FIELD INHOMOGENEITY COMPENSATION USING STRUCTURED LOW-RANK MATRIX COMPLETION

Echo-planar imaging (EPI), which is the main workhorse of functional MRI, suffers from field inhomogeneity-induced geometric distortions. The amount of distortion is proportional to the readout duration, which restricts the maximum achievable spatial resolution. The spatially varying nature of the T 2 * decay makes it challenging for EPI schemes with a single echo time to obtain good sensitivity to functional activations in different brain regions. Despite the use of parallel MRI and multislice acceleration, the number of different echo times that can be acquired in a reasonable TR is limited. The main focus of this work is to introduce a rosette-based acquisition scheme and a structured low-rank reconstruction algorithm to overcome the above challenges. The proposed scheme exploits the exponential structure of the time series to recover distortion-free images from several echoes simultaneously.

Structured Low-Rank Algorithms: Theory, Magnetic Resonance Applications, and Links to Machine Learning

In this survey, we provide a detailed review of recent advances in the recovery of continuous domain multidimensional signals from their few non-uniform (multichannel) measurements using structured low-rank matrix completion formulation. This framework is centered on the fundamental duality between the compactness (e.g., sparsity) of the continuous signal and the rank of a structured matrix, whose entries are functions of the signal. This property enables the reformulation of the signal recovery as a low-rank structured matrix completion, which comes with performance guarantees. We will also review fast algorithms that are comparable in complexity to current compressed sensing methods, which enables the application of the framework to large-scale magnetic resonance (MR) recovery problems. The remarkable flexibility of the formulation can be used to exploit signal properties that are difficult to capture by current sparse and low-rank optimization strategies. We demonstrate the utility of the framework in a wide range of MR imaging (MRI) applications, including highly accelerated imaging, calibration-free acquisition, MR artifact correction, and ungated dynamic MRI.

Improved MUSSELS reconstruction for high-resolution multi-shot diffusion weighted imaging

PURPOSE

MUSSELS is a one-step iterative reconstruction method for multishot diffusion weighted (msDW) imaging. The current work presents an efficient implementation, termed IRLS MUSSELS, that enables faster reconstruction to enhance its utility for high-resolution diffusion MRI studies.

METHODS

The recently proposed MUSSELS reconstruction belongs to a new class of parallel imaging-based methods that recover artifact-free DWIs from msDW data without needing phase compensation. The reconstruction is achieved via structured low-rank matrix completion algorithms, which are computationally demanding due to the large size of the Hankel matrices and their associated computations involving singular value decompositions. Because of this, computational demands of the MUSSELS reconstruction scales as the matrix size and the number of shots increases, which hinders its practical utility for high-resolution applications. In this work, we derive a computationally efficient MUSSELS formulation by modifying the iterative reweighted least squares (IRLS) method that were proposed earlier to solve such problems. Using whole-brain in vivo data, we show the utility of the IRLS MUSSELS for routine high-resolution studies with reduced computational burden.

RESULTS

IRLS MUSSELS provides about five times faster reconstruction for matrix sizes 192 × 192 and 256 × 256 compared to the earlier MUSSELS implementation. The widely employed conjugate symmetry priors can also be incorporated into IRLS MUSSELS to reduce blurring of the partial Fourier acquisitions, without incurring much computational burden.

CONCLUSIONS

The proposed method is observed to be computationally efficient to enable routine high-resolution studies. The computational complexity matches the traditional msDWI reconstruction methods and provides improved reconstruction results with the additional constraints.

SMS MUSSELS: A navigator-free reconstruction for simultaneous multi-slice-accelerated multi-shot diffusion weighted imaging

PURPOSE

To introduce a novel reconstruction method for simultaneous multi-slice (SMS)-accelerated multi-shot diffusion weighted imaging (ms-DWI).

METHODS

SMS acceleration using blipped-CAIPI schemes have been proposed to speed up the acquisition of ms-DWIs. The reconstruction of the data requires (a) phase compensation to combine data from different shots and (b) slice unfolding to separate the data of different slices. The traditional approaches first estimate the phase maps corresponding to each shot and slice which are then employed to iteratively recover the slice unfolded DWIs without phase artifacts. In contrast, the proposed reconstruction directly recovers the slice-unfolded k-space data of the multiple shots for each slice in a single-step recovery scheme. The proposed method is enabled by the low-rank property inherent in the k-space samples of ms-DW acquisition. This enabled to formulate a joint recovery scheme that simultaneously (a) unfolds the k-space data of each slice using a SENSE-based scheme and (b) recover the missing k-space samples in each slice of the multi-shot acquisition employing a structured low-rank matrix completion. Additional smoothness regularization is also utilized for higher acceleration factors. The proposed joint recovery is tested on simulated and in vivo data and compared to similar un-navigated methods.

RESULTS

Our experiments show effective slice unfolding and successful recovery of DWIs with minimal phase artifacts using the proposed method. The performance is comparable to existing methods at low acceleration factors and better than existing methods for higher acceleration factors.

CONCLUSIONS

For the slice accelerations considered in this study, the proposed method can successfully recover DWIs from SMS-accelerated ms-DWI acquisitions.