### Abstract

The authors describe and demonstrate a hierarchical reconstruction algorithm for use in noisy and limited-angle or sparse-angle tomography. The algorithm estimates the object's mass, center of mass, and convex hull from the available projections, and uses this information, along with fundamental mathematical constraints, to estimate a full set of smoothed projections. The mass and center of mass are estimated using a maximum-likelihood (ML) estimator derived from the principles of consistency of the Radon transform. The convex hull estimate is produced by first estimating the positions of support lines of the object from each available projection and then estimating the overall convex hull using ML or maximum a posteriori (MAP) techniques. The position of two support lines from a single projection is estimated using either a generalized-likelihood-ratio technique for estimating jumps in linear systems or a support-width penalty method that uses Akaike's model-order estimation technique.

Original language | English (US) |
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Pages (from-to) | 1468-1471 |

Number of pages | 4 |

Journal | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |

Volume | 3 |

State | Published - Dec 1 1989 |

Externally published | Yes |

Event | 1989 International Conference on Acoustics, Speech, and Signal Processing - Glasgow, Scotland Duration: May 23 1989 → May 26 1989 |

### ASJC Scopus subject areas

- Software
- Signal Processing
- Electrical and Electronic Engineering

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## Cite this

*ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings*,

*3*, 1468-1471.