3D variable-density SPARKLING trajectories for high-resolution T2*-weighted magnetic resonance imaging.

We have recently proposed a new optimization algorithm called SPARKLING (Spreading Projection Algorithm for Rapid K-space sampLING) to design efficient compressive sampling patterns for magnetic resonance imaging (MRI). This method has a few advantages over conventional non-Cartesian trajectories such as radial lines or spirals: i) it allows to sample the k-space along any arbitrary density while the other two are restricted to radial densities and ii) it optimizes the gradient waveforms for a given readout time. Here, we introduce an extension of the SPARKLING method for 3D imaging by considering both stacks-of-SPARKLING and fully 3D SPARKLING trajectories. Our method allowed to achieve an isotropic resolution of 600 µm in just 45 seconds for T2∗-weighted ex vivo brain imaging at 7 Tesla over a field-of-view of 200 × 200 × 140 mm3 . Preliminary in vivo human brain data shows that a stack-of-SPARKLING is less subject to off-resonance artifacts than a stack-of-spirals.

SPARKLING: variable-density k-space filling curves for accelerated T2* -weighted MRI.

PURPOSE: To present a new optimition-driven design of optimal k-space trajectories in the context of compressed sensing: Spreading Projection Algorithm for Rapid K-space sampLING (SPARKLING). THEORY: The SPARKLING algorithm is a versatile method inspired from stippling techniques that automatically generates optimized sampling patterns compatible with MR hardware constraints on maximum gradient amplitude and slew rate. These non-Cartesian sampling curves are designed to comply with key criteria for optimal sampling: a controlled distribution of samples (e.g., variable density) and a locally uniform k-space coverage. METHODS: Ex vivo and in vivo prospective T2* -weighted acquisitions were performed on a 7-Tesla scanner using the SPARKLING trajectories for various setups and target densities. Our method was compared to radial and variable-density spiral trajectories for high-resolution imaging. RESULTS: Combining sampling efficiency with compressed sensing, the proposed sampling patterns allowed up to 20-fold reductions in MR scan time (compared to fully sampled Cartesian acquisitions) for two-dimensional T2* -weighted imaging without deterioration of image quality, as demonstrated by our experimental results at 7 Tesla on in vivo human brains for a high in-plane resolution of 390 µm. In comparison to existing non-Cartesian sampling strategies, the proposed technique also yielded superior image quality. CONCLUSIONS: The proposed optimization-driven design of k-space trajectories is a versatile framework that is able to enhance MR sampling performance in the context of compressed sensing.

Calibration-Less Multi-Coil Compressed Sensing Magnetic Resonance Image Reconstruction Based on OSCAR Regularization.

Over the last decade, the combination of compressed sensing (CS) with acquisition over multiple receiver coils in magnetic resonance imaging (MRI) has allowed the emergence of faster scans while maintaining a good signal-to-noise ratio (SNR). Self-calibrating techniques, such as ESPiRIT, have become the standard approach to estimating the coil sensitivity maps prior to the reconstruction stage. In this work, we proceed differently and introduce a new calibration-less multi-coil CS reconstruction method. Calibration-less techniques no longer require the prior extraction of sensitivity maps to perform multi-coil image reconstruction but usually alternate estimation sensitivity map estimation and image reconstruction. Here, to get rid of the nonconvexity of the latter approach we reconstruct as many MR images as the number of coils. To compensate for the ill-posedness of this inverse problem, we leverage structured sparsity of the multi-coil images in a wavelet transform domain while adapting to variations in SNR across coils owing to the OSCAR (octagonal shrinkage and clustering algorithm for regression) regularization. Coil-specific complex-valued MR images are thus obtained by minimizing a convex but nonsmooth objective function using the proximal primal-dual Condat-Vù algorithm. Comparison and validation on retrospective Cartesian and non-Cartesian studies based on the Brain fastMRI data set demonstrate that the proposed reconstruction method outperforms the state-of-the-art (ℓ1-ESPIRiT, calibration-less AC-LORAKS and CaLM methods) significantly on magnitude images for the T1 and FLAIR contrasts. Additionally, further validation operated on 8 to 20-fold prospectively accelerated high-resolution ex vivo human brain MRI data collected at 7 Tesla confirms the retrospective results. Overall, OSCAR-based regularization preserves phase information more accurately (both visually and quantitatively) compared to other approaches, an asset that can only be assessed on real prospective experiments.