# An Approximate Message Passing Algorithm for Rapid Parameter-Free Compressed Sensing MRI

arXiv: https://arxiv.org/abs/1911.01234 · HTML: https://mlsanity.com/paper/1911.01234/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2019.

## Built on by (most cited first, 2 of 2)

- [Building Conformal Prediction Intervals with Approximate Message Passing](https://mlsanity.com/paper/2410.16493/) (2024)
- [Tuning-free multi-coil compressed sensing MRI with Parallel Variable Density Approximate Message Passing (P-VDAMP)](https://mlsanity.com/paper/2203.04180/) (2022)

## Abstract (arXiv)

For certain sensing matrices, the Approximate Message Passing (AMP) algorithm efficiently reconstructs undersampled signals. However, in Magnetic Resonance Imaging (MRI), where Fourier coefficients of a natural image are sampled with variable density, AMP encounters convergence problems. In response we present an algorithm based on Orthogonal AMP constructed specifically for variable density partial Fourier sensing matrices. For the first time in this setting a state evolution has been observed. A practical advantage of state evolution is that Stein's Unbiased Risk Estimate (SURE) can be effectively implemented, yielding an algorithm with no free parameters. We empirically evaluate the effectiveness of the parameter-free algorithm on simulated data and find that it converges over 5x faster and to a lower mean-squared error solution than Fast Iterative Shrinkage-Thresholding (FISTA).