### 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 |
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Title of host publication | Proceedings of the Annual Conference on Engineering in Medicine and Biology |

Place of Publication | Piscataway, NJ, United States |

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 |

### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Bioengineering

### Cite this

*Proceedings of the Annual Conference on Engineering in Medicine and Biology*(pt 1 ed., pp. 381-382). Piscataway, NJ, United States: Publ by IEEE.

**A method of image reconstruction using spline harmonics.** / Cheung, W. K.; Herman, G. T.; Markoe, Arnold.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Annual Conference on Engineering in Medicine and Biology.*pt 1 edn, Publ by IEEE, Piscataway, NJ, United States, pp. 381-382, Proceedings of the 12th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Philadelphia, PA, USA, 11/1/90.

}

TY - GEN

T1 - A method of image reconstruction using spline harmonics

AU - Cheung, W. K.

AU - Herman, G. T.

AU - Markoe, Arnold

PY - 1990/12/1

Y1 - 1990/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0025532933&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025532933&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0879425598

SP - 381

EP - 382

BT - Proceedings of the Annual Conference on Engineering in Medicine and Biology

PB - Publ by IEEE

CY - Piscataway, NJ, United States

ER -