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

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...

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Bibliographic Details
Published in:Proceedings - International Conference on Image Processing pp. 91 - 95
Main Authors: Millard, Charles, Hess, Aaron T, Mailhe, Boris, Tanner, Jared
Format: Conference Proceeding
Language:English
Published: IEEE 01.10.2020
Subjects:
Approximate Message Passing
Approximation algorithms
Compressed sensing
Image reconstruction
Magnetic resonance imaging
Message passing
Sensors
Stein's Unbiased Risk Estimate
ISSN:2381-8549
Online Access:Get full text
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Summary: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).
ISSN:2381-8549
DOI:10.1109/ICIP40778.2020.9190668