### Abstract

An approach to image reconstruction using spline harmonics is formulated. It is shown that a function whose Radon transform is a spline harmonic can be recovered using a closed-form expression from the finite number of expansion coefficients describing the spline harmonic. The significance of this result comes from the fact that, in the appropriate Sobolev spaces, the spline harmonics are dense in the range of the Radon transform and the inverse Radon transform is continuous. Thus, one can expect to fit actual projection data with a spline harmonic as tightly as is justified by the noise in the data and then have the resulting reconstruction be consistent with the data. The authors outline the derivation of the main formulae in this approach and discuss the constraints and considerations applicable to the various parameters used.

Original language | English (US) |
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Title of host publication | Biomedical Engineering Perspectives |

Subtitle of host publication | Health Care Technologies for the 1990's and Beyond |

Publisher | Publ by IEEE |

Pages | 381-382 |

Number of pages | 2 |

Edition | pt 1 |

ISBN (Print) | 0879425598 |

State | Published - Dec 1 1990 |

Externally published | Yes |

Event | Proceedings of the 12th Annual International Conference of the IEEE Engineering in Medicine and Biology Society - Philadelphia, PA, USA Duration: Nov 1 1990 → Nov 4 1990 |

### Publication series

Name | Proceedings of the Annual Conference on Engineering in Medicine and Biology |
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Number | pt 1 |

ISSN (Print) | 0589-1019 |

### Other

Other | Proceedings of the 12th Annual International Conference of the IEEE Engineering in Medicine and Biology Society |
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City | Philadelphia, PA, USA |

Period | 11/1/90 → 11/4/90 |

### ASJC Scopus subject areas

- Signal Processing
- Biomedical Engineering
- Computer Vision and Pattern Recognition
- Health Informatics

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## Cite this

*Biomedical Engineering Perspectives: Health Care Technologies for the 1990's and Beyond*(pt 1 ed., pp. 381-382). (Proceedings of the Annual Conference on Engineering in Medicine and Biology; No. pt 1). Publ by IEEE.