Accelerating compressed sensing in parallel imaging reconstructions using an efficient circulant preconditioner for cartesian trajectories.
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| Title: | Accelerating compressed sensing in parallel imaging reconstructions using an efficient circulant preconditioner for cartesian trajectories. |
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| Authors: | Koolstra, Kirsten1, van Gemert, Jeroen2 J.H.F.vanGemert-1@tudelft.nl, Börnert, Peter1,3, Webb, Andrew1, Remis, Rob2 |
| Source: | Magnetic Resonance in Medicine. Jan2019, Vol. 81 Issue 1, p670-685. 16p. |
| Abstract: | Purpose: Design of a preconditioner for fast and efficient parallel imaging (PI) and compressed sensing (CS) reconstructions for Cartesian trajectories. Theory: PI and CS reconstructions become time consuming when the problem size or the number of coils is large, due to the large linear system of equations that has to be solved in ℓ1 and ℓ2‐norm based reconstruction algorithms. Such linear systems can be solved efficiently using effective preconditioning techniques. Methods: In this article we construct such a preconditioner by approximating the system matrix of the linear system, which comprises the data fidelity and includes total variation and wavelet regularization, by a matrix that is block circulant with circulant blocks. Due to this structure, the preconditioner can be constructed quickly and its inverse can be evaluated fast using only two fast Fourier transformations. We test the performance of the preconditioner for the conjugate gradient method as the linear solver, integrated into the thyc=10well‐establishedthyc Split Bregman algorithm. Results: The designed circulant preconditioner reduces the number of iterations required in the conjugate gradient method by almost a factor of 5. The speed up results in a total acceleration factor of approximately 2.5 for the entire reconstruction algorithm when implemented in MATLAB, while the initialization time of the preconditioner is negligible. Conclusion: The proposed preconditioner reduces the reconstruction time for PI and CS in a Split Bregman implementation without compromising reconstruction stability and can easily handle large systems since it is thyc=10Fourier‐based,thyc allowing for efficient computations. [ABSTRACT FROM AUTHOR] |
| Copyright of Magnetic Resonance in Medicine is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
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| Header | DbId: egs DbLabel: Engineering Source An: 133236021 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Accelerating compressed sensing in parallel imaging reconstructions using an efficient circulant preconditioner for cartesian trajectories. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Koolstra%2C+Kirsten%22">Koolstra, Kirsten</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22van+Gemert%2C+Jeroen%22">van Gemert, Jeroen</searchLink><relatesTo>2</relatesTo><i> J.H.F.vanGemert-1@tudelft.nl</i><br /><searchLink fieldCode="AR" term="%22Börnert%2C+Peter%22">Börnert, Peter</searchLink><relatesTo>1,3</relatesTo><br /><searchLink fieldCode="AR" term="%22Webb%2C+Andrew%22">Webb, Andrew</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Remis%2C+Rob%22">Remis, Rob</searchLink><relatesTo>2</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Magnetic+Resonance+in+Medicine%22">Magnetic Resonance in Medicine</searchLink>. Jan2019, Vol. 81 Issue 1, p670-685. 16p. – Name: Abstract Label: Abstract Group: Ab Data: Purpose: Design of a preconditioner for fast and efficient parallel imaging (PI) and compressed sensing (CS) reconstructions for Cartesian trajectories. Theory: PI and CS reconstructions become time consuming when the problem size or the number of coils is large, due to the large linear system of equations that has to be solved in ℓ1 and ℓ2‐norm based reconstruction algorithms. Such linear systems can be solved efficiently using effective preconditioning techniques. Methods: In this article we construct such a preconditioner by approximating the system matrix of the linear system, which comprises the data fidelity and includes total variation and wavelet regularization, by a matrix that is block circulant with circulant blocks. Due to this structure, the preconditioner can be constructed quickly and its inverse can be evaluated fast using only two fast Fourier transformations. We test the performance of the preconditioner for the conjugate gradient method as the linear solver, integrated into the thyc=10well‐establishedthyc Split Bregman algorithm. Results: The designed circulant preconditioner reduces the number of iterations required in the conjugate gradient method by almost a factor of 5. The speed up results in a total acceleration factor of approximately 2.5 for the entire reconstruction algorithm when implemented in MATLAB, while the initialization time of the preconditioner is negligible. Conclusion: The proposed preconditioner reduces the reconstruction time for PI and CS in a Split Bregman implementation without compromising reconstruction stability and can easily handle large systems since it is thyc=10Fourier‐based,thyc allowing for efficient computations. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Magnetic Resonance in Medicine is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/mrm.27371 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 670 Titles: – TitleFull: Accelerating compressed sensing in parallel imaging reconstructions using an efficient circulant preconditioner for cartesian trajectories. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Koolstra, Kirsten – PersonEntity: Name: NameFull: van Gemert, Jeroen – PersonEntity: Name: NameFull: Börnert, Peter – PersonEntity: Name: NameFull: Webb, Andrew – PersonEntity: Name: NameFull: Remis, Rob IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan2019 Type: published Y: 2019 Identifiers: – Type: issn-print Value: 07403194 Numbering: – Type: volume Value: 81 – Type: issue Value: 1 Titles: – TitleFull: Magnetic Resonance in Medicine Type: main |
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