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

TL;DR

This paper introduces P-VDAMP, a novel multi-coil MRI reconstruction algorithm that automatically tunes parameters using state evolution and SURE, achieving high-quality results without manual tuning.

Contribution

The authors extend VDAMP to multi-coil MRI, creating P-VDAMP, which uniquely obeys a state evolution for automatic parameter tuning in compressed sensing MRI.

Findings

P-VDAMP matches the quality of optimally tuned FISTA.

P-VDAMP outperforms existing tuning-free methods in robustness.

The algorithm converges efficiently on various MRI datasets.

Abstract

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.