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

arXiv: https://arxiv.org/abs/2203.04180 · HTML: https://mlsanity.com/paper/2203.04180/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 59 references that are in the map.
- First posted on arXiv 8 Mar 2022.

## Builds on (most cited first, 10 of 10)

- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Plug and play methods for magnetic resonance imaging (long version)](https://mlsanity.com/paper/1903.08616/) (2019)
- [From Denoising to Compressed Sensing](https://mlsanity.com/paper/1406.4175/) (2014)
- [Learned D-AMP: Principled Neural Network based Compressive Image Recovery](https://mlsanity.com/paper/1704.06625/) (2017)
- [On the Empirical Effect of Gaussian Noise in Under-sampled MRI Reconstruction](https://mlsanity.com/paper/1610.00410/) (2016)
- [D-VDAMP: Denoising-based Approximate Message Passing for Compressive MRI](https://mlsanity.com/paper/2010.13211/) (2020)
- [SUREMap: Predicting Uncertainty in CNN-based Image Reconstruction Using Stein's Unbiased Risk Estimate](https://mlsanity.com/paper/2010.13214/) (2020)
- [An Approximate Message Passing Algorithm for Rapid Parameter-Free Compressed Sensing MRI](https://mlsanity.com/paper/1911.01234/) (2019)
- [Approximate Message Passing with a Colored Aliasing Model for Variable Density Fourier Sampled Images](https://mlsanity.com/paper/2003.02701/) (2020)
- [Parameterless Optimal Approximate Message Passing](https://mlsanity.com/paper/1311.0035/) (2013)

## Built on by (most cited first, 1 of 1)

- [Denoising Generalized Expectation-Consistent Approximation for MR Image Recovery](https://mlsanity.com/paper/2206.05049/) (2022)

## Abstract (arXiv)

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.