### Abstract

Magnetic resonance signals that have very short relaxation times are conveniently sampled in a spherical fashion. We derive a least squares framework for reconstructing three-dimensional source distribution images from such data. Using a finite-series approach, the image is represented as a weighted sum of translated Kaiser-Bessel window functions. The Radon transform thereof establishes the connection with the projection data that one can obtain from the radial sampling trajectories. The resulting linear system of equations is sparse, but quite large. To reduce the size of the problem, we introduce focus of attention. Based on the theory of support functions, this data-driven preprocessing scheme eliminates equations and unknowns that merely represent the background. The image reconstruction and the focus of attention both require a least squares solution to be computed. We describe a projected gradient approach that facilitates a non-negativity constrained version of the powerful LSQR algorithm. In order to ensure reasonable execution times, the least squares computation can be distributed across a network of PCs and/or workstations. We discuss how to effectively parallelize the NN-LSQR algorithm. We close by presenting results from experimental work that addresses both computational issues and image quality using a mathematical phantom.

Original language | English (US) |
---|---|

Pages (from-to) | 888-898 |

Number of pages | 11 |

Journal | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 4322 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2001 |

Event | Medical Imaging 2001 Image Processing - San Diego, CA, United States Duration: Feb 19 2001 → Feb 22 2001 |

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### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering

### Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*,

*4322*(2), 888-898. https://doi.org/10.1117/12.431168

**Least squares framework for projection MRI reconstruction.** / Gregor, Jens; Rannou, F. R.

Research output: Contribution to journal › Conference article

*Proceedings of SPIE - The International Society for Optical Engineering*, vol. 4322, no. 2, pp. 888-898. https://doi.org/10.1117/12.431168

}

TY - JOUR

T1 - Least squares framework for projection MRI reconstruction

AU - Gregor, Jens

AU - Rannou, F. R.

PY - 2001/1/1

Y1 - 2001/1/1

N2 - Magnetic resonance signals that have very short relaxation times are conveniently sampled in a spherical fashion. We derive a least squares framework for reconstructing three-dimensional source distribution images from such data. Using a finite-series approach, the image is represented as a weighted sum of translated Kaiser-Bessel window functions. The Radon transform thereof establishes the connection with the projection data that one can obtain from the radial sampling trajectories. The resulting linear system of equations is sparse, but quite large. To reduce the size of the problem, we introduce focus of attention. Based on the theory of support functions, this data-driven preprocessing scheme eliminates equations and unknowns that merely represent the background. The image reconstruction and the focus of attention both require a least squares solution to be computed. We describe a projected gradient approach that facilitates a non-negativity constrained version of the powerful LSQR algorithm. In order to ensure reasonable execution times, the least squares computation can be distributed across a network of PCs and/or workstations. We discuss how to effectively parallelize the NN-LSQR algorithm. We close by presenting results from experimental work that addresses both computational issues and image quality using a mathematical phantom.

AB - Magnetic resonance signals that have very short relaxation times are conveniently sampled in a spherical fashion. We derive a least squares framework for reconstructing three-dimensional source distribution images from such data. Using a finite-series approach, the image is represented as a weighted sum of translated Kaiser-Bessel window functions. The Radon transform thereof establishes the connection with the projection data that one can obtain from the radial sampling trajectories. The resulting linear system of equations is sparse, but quite large. To reduce the size of the problem, we introduce focus of attention. Based on the theory of support functions, this data-driven preprocessing scheme eliminates equations and unknowns that merely represent the background. The image reconstruction and the focus of attention both require a least squares solution to be computed. We describe a projected gradient approach that facilitates a non-negativity constrained version of the powerful LSQR algorithm. In order to ensure reasonable execution times, the least squares computation can be distributed across a network of PCs and/or workstations. We discuss how to effectively parallelize the NN-LSQR algorithm. We close by presenting results from experimental work that addresses both computational issues and image quality using a mathematical phantom.

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UR - http://www.scopus.com/inward/citedby.url?scp=0034846489&partnerID=8YFLogxK

U2 - 10.1117/12.431168

DO - 10.1117/12.431168

M3 - Conference article

VL - 4322

SP - 888

EP - 898

JO - Proceedings of SPIE - The International Society for Optical Engineering

JF - Proceedings of SPIE - The International Society for Optical Engineering

SN - 0277-786X

IS - 2

ER -