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

TL;DR

This paper introduces an Orthogonal AMP algorithm tailored for variable density Fourier sensing in MRI, achieving faster convergence and lower error without parameter tuning, validated through simulations.

Contribution

It presents the first application of state evolution and parameter-free AMP in MRI with variable density sampling, improving reconstruction speed and accuracy.

Findings

Converges over 5 times faster than FISTA

Achieves lower mean-squared error in reconstructions

Successfully applies state evolution to MRI sampling matrices

Abstract

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).