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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| Vydáno v: | Proceedings - International Conference on Image Processing s. 91 - 95 |
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| Jazyk: | angličtina |
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IEEE
01.10.2020
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| ISSN: | 2381-8549 |
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| 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). |
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| AbstractList | 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). |
| Author | Tanner, Jared Hess, Aaron T Millard, Charles Mailhe, Boris |
| Author_xml | – sequence: 1 givenname: Charles surname: Millard fullname: Millard, Charles organization: Mathematical Institute, University of Oxford,UK – sequence: 2 givenname: Aaron T surname: Hess fullname: Hess, Aaron T organization: University of Oxford,Oxford Centre for Clinical Magnetic Resonance,UK – sequence: 3 givenname: Boris surname: Mailhe fullname: Mailhe, Boris organization: Siemens Healthineers,Princeton,NJ,USA – sequence: 4 givenname: Jared surname: Tanner fullname: Tanner, Jared organization: Mathematical Institute, University of Oxford,UK |
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| Snippet | For certain sensing matrices, the Approximate Message Passing (AMP) algorithm efficiently reconstructs undersampled signals. However, in Magnetic Resonance... |
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| StartPage | 91 |
| SubjectTerms | Approximate Message Passing Approximation algorithms Compressed sensing Image reconstruction Magnetic resonance imaging Message passing Sensors Stein's Unbiased Risk Estimate |
| Title | An Approximate Message Passing Algorithm For Rapid Parameter-Free Compressed Sensing MRI |
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