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Magnetic Resonance Imaging (MRI) has excellent soft tissue contrast but is hindered by an inherently slow data acquisition process. Compressed sensing, which reconstructs sparse signals from incoherently sampled data, has been widely applied to accelerate MRI acquisitions. Compressed sensing MRI requires one or more model parameters to be tuned, which is usually done by hand, giving sub-optimal tuning in general. To address this issue, we build on previous work by the authors on the single-coil Variable Density Approximate Message Passing (VDAMP) algorithm, extending the framework to multiple receiver coils to propose the Parallel VDAMP (P-VDAMP) algorithm. For Bernoulli random variable density sampling, P-VDAMP obeys a "state evolution", where the intermediate per-iteration image estimate is distributed according to the ground truth corrupted by a zero-mean Gaussian vector with approximately known covariance. To our knowledge, P-VDAMP is the first algorithm for multi-coil MRI data that obeys a state evolution with accurately tracked parameters. We leverage state evolution to automatically tune sparse parameters on-the-fly with Stein's Unbiased Risk Estimate (SURE). P-VDAMP is evaluated on brain, knee and angiogram datasets and compared with four variants of the Fast Iterative Shrinkage-Thresholding algorithm (FISTA), including two tuning-free variants from the literature. The proposed method is found to have a similar reconstruction quality and time to convergence as FISTA with an optimally tuned sparse weighting and offers substantial robustness and reconstruction quality improvements over competing tuning-free methods., Comment: 10 pages, 9 figures, submitted to IEEE TMI on 26th April 2022

Purpose: 3D Time-of-flight (TOF) MR Angiography (MRA) can accurately visualize the intracranial vasculature, but is limited by long acquisition times. Compressed sensing (CS) reconstruction can be used to substantially accelerate acquisitions. The quality of those reconstructions depends on the undersampling patterns used in the acquisitions. In this work, optimized sets of undersampling parameters using various acceleration factors for Cartesian 3D TOF-MRA are established. Methods: Fully-sampled datasets acquired at 7T were retrospectively undersampled using variable-density Poisson-disk sampling with various autocalibration region sizes, polynomial orders, and acceleration factors. The accuracy of reconstructions from the different undersampled datasets was assessed using the vessel-masked structural similarity index. Results were compared for four imaging volumes, acquired from two different subjects. Optimized undersampling parameters were validated using additional prospectively undersampled datasets. Results: For all acceleration factors, using a fully-sampled calibration area of 12x12 k-space lines and a polynomial order of around 2-2.4 resulted in the highest image quality. The importance of sampling parameter optimization was found to increase for higher acceleration factors. The results were consistent across resolutions and regions of interest with vessels of varying sizes and tortuosity. In prospectively undersampled acquisitions, using optimized undersampling parameters resulted in a 7.2% increase in the number of visible small vessels at R = 7.2. Conclusion: The image quality of CS TOF-MRA can be improved by appropriate choice of undersampling parameters. The optimized sets of parameters are independent of the acceleration factor., Comment: Manuscript to be submitted to Magnetic Resonance in Medicine

Additional file 1: Supplementary material.