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Magnetic Resonance Imaging (MRI) has excellent soft tissue contrast but ishindered by an inherently slow data acquisition process. Compressed sensing,which reconstructs sparse signals from incoherently sampled data, has beenwidely applied to accelerate MRI acquisitions. Compressed sensing MRI requiresone or more model parameters to be tuned, which is usually done by hand, givingsub-optimal tuning in general. To address this issue, we build on previous workby the authors on the single-coil Variable Density Approximate Message Passing(VDAMP) algorithm, extending the framework to multiple receiver coils topropose the Parallel VDAMP (P-VDAMP) algorithm. For Bernoulli random variabledensity sampling, P-VDAMP obeys a "state evolution", where the intermediateper-iteration image estimate is distributed according to the ground truthcorrupted by a zero-mean Gaussian vector with approximately known covariance.To our knowledge, P-VDAMP is the first algorithm for multi-coil MRI data thatobeys a state evolution with accurately tracked parameters. We leverage stateevolution to automatically tune sparse parameters on-the-fly with Stein'sUnbiased Risk Estimate (SURE). P-VDAMP is evaluated on brain, knee andangiogram datasets and compared with four variants of the Fast IterativeShrinkage-Thresholding algorithm (FISTA), including two tuning-free variantsfrom the literature. The proposed method is found to have a similarreconstruction quality and time to convergence as FISTA with an optimally tunedsparse weighting and offers substantial robustness and reconstruction qualityimprovements over competing tuning-free methods.

Tuning-free multi-coil compressed sensing MRI with Parallel Variable Density Approximate Message Passing (P-VDAMP)