Approximate message passing for compressed sensing magnetic resonance imaging
<p>Magnetic Resonance Imaging (MRI) is a non-invasive, non-ionising imaging modality with unrivalled soft tissue contrast. A key consideration for MRI is data acquisition time, which is limited by inherent technological and physiological constraints. Compressed sensing is a relatively recent f...
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| Format: | Thesis |
| Language: | English |
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2021
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| _version_ | 1826298739864633344 |
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| author | Millard, C |
| author2 | Tanner , J |
| author_facet | Tanner , J Millard, C |
| author_sort | Millard, C |
| collection | OXFORD |
| description | <p>Magnetic Resonance Imaging (MRI) is a non-invasive, non-ionising imaging modality with unrivalled soft tissue contrast. A key consideration for MRI is data acquisition time, which is limited by inherent technological and physiological constraints. Compressed sensing is a relatively recent framework that can reduce the MRI acquisition time by undersampling randomly and exploiting presumed redundancies in the data.</p>
<p>The Approximate Message Passing (AMP) algorithm is an iterative compressed sensing method that efficiently reconstructs signals that have been sampled with i.i.d. sub-Gaussian sensing matrices. However, when Fourier coefficients of a signal with non-uniform spectral density are sampled, such as in MRI, AMP performs poorly in practice.</p>
<p>In response, this thesis proposes the Variable Density Approximate Message Passing (VDAMP) algorithm for undersampled MRI data. We present three versions of VDAMP: single-coil VDAMP, where receiver coil sensitivities are ignored, Parallel-VDAMP (P-VDAMP), which includes coil sensitivities, and Denoising-P-VDAMP (D-P-VDAMP), which incorporates the statistical modelling capabilities of neural networks. Central to VDAMP is a property that we term "coloured state evolution", where the difference between the intermediate image estimate at a given iteration and the ground truth is distributed according to a zero-mean Gaussian with known covariance. We demonstrate that coloured state evolution can be leveraged to yield an algorithm that converges rapidly, and to a competitive reconstruction quality, without the need to hand-tune model parameters.</p> |
| first_indexed | 2024-03-07T04:51:25Z |
| format | Thesis |
| id | oxford-uuid:d5197d8e-369e-4d56-8384-dc70c445a424 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:51:25Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | oxford-uuid:d5197d8e-369e-4d56-8384-dc70c445a4242022-03-27T08:23:30ZApproximate message passing for compressed sensing magnetic resonance imagingThesishttp://purl.org/coar/resource_type/c_db06uuid:d5197d8e-369e-4d56-8384-dc70c445a424Magnetic resonance imagingSignal processingNumerical analysisImage reconstructionMathematicsEnglishHyrax Deposit2021Millard, CTanner , JHess, AMailhe, B<p>Magnetic Resonance Imaging (MRI) is a non-invasive, non-ionising imaging modality with unrivalled soft tissue contrast. A key consideration for MRI is data acquisition time, which is limited by inherent technological and physiological constraints. Compressed sensing is a relatively recent framework that can reduce the MRI acquisition time by undersampling randomly and exploiting presumed redundancies in the data.</p> <p>The Approximate Message Passing (AMP) algorithm is an iterative compressed sensing method that efficiently reconstructs signals that have been sampled with i.i.d. sub-Gaussian sensing matrices. However, when Fourier coefficients of a signal with non-uniform spectral density are sampled, such as in MRI, AMP performs poorly in practice.</p> <p>In response, this thesis proposes the Variable Density Approximate Message Passing (VDAMP) algorithm for undersampled MRI data. We present three versions of VDAMP: single-coil VDAMP, where receiver coil sensitivities are ignored, Parallel-VDAMP (P-VDAMP), which includes coil sensitivities, and Denoising-P-VDAMP (D-P-VDAMP), which incorporates the statistical modelling capabilities of neural networks. Central to VDAMP is a property that we term "coloured state evolution", where the difference between the intermediate image estimate at a given iteration and the ground truth is distributed according to a zero-mean Gaussian with known covariance. We demonstrate that coloured state evolution can be leveraged to yield an algorithm that converges rapidly, and to a competitive reconstruction quality, without the need to hand-tune model parameters.</p> |
| spellingShingle | Magnetic resonance imaging Signal processing Numerical analysis Image reconstruction Mathematics Millard, C Approximate message passing for compressed sensing magnetic resonance imaging |
| title | Approximate message passing for compressed sensing magnetic resonance imaging |
| title_full | Approximate message passing for compressed sensing magnetic resonance imaging |
| title_fullStr | Approximate message passing for compressed sensing magnetic resonance imaging |
| title_full_unstemmed | Approximate message passing for compressed sensing magnetic resonance imaging |
| title_short | Approximate message passing for compressed sensing magnetic resonance imaging |
| title_sort | approximate message passing for compressed sensing magnetic resonance imaging |
| topic | Magnetic resonance imaging Signal processing Numerical analysis Image reconstruction Mathematics |
| work_keys_str_mv | AT millardc approximatemessagepassingforcompressedsensingmagneticresonanceimaging |