### Abstract

This paper derives fundamental performance bounds for estimating 3-D parametric surfaces in inverse problems. Un-like conventional pixel-based image reconstruction approaches, our problem is reconstruction of the shape of binary or homogeneous objects. The fundamental uncertainty of such estimation problems can be represented by global confidence regions, which facilitate geometric inference and optimization of the imaging system. Compared to two-dimensional global confidence region analysis in our previous work, computation of the probability that the entire 3-D surface estimate lies within the confidence region is, however, more challenging, because a surface estimate is an inhomogeneous random field continuously indexed by a two-dimensional index set. We derive an approximate lower bound to this probability using the so-called tube formula for the tail probability of a Gaussian random field. Simulation results demonstrate the tightness of the resulting bound and the usefulness of 3-D global confidence region approach.

Original language | English (US) |
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Title of host publication | 2005 IEEE/SP 13th Workshop on Statistical Signal Processing - Book of Abstracts |

Pages | 471-476 |

Number of pages | 6 |

State | Published - Dec 1 2005 |

Event | 2005 IEEE/SP 13th Workshop on Statistical Signal Processing - Bordeaux, France Duration: Jul 17 2005 → Jul 20 2005 |

### Publication series

Name | IEEE Workshop on Statistical Signal Processing Proceedings |
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Volume | 2005 |

### Other

Other | 2005 IEEE/SP 13th Workshop on Statistical Signal Processing |
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Country | France |

City | Bordeaux |

Period | 7/17/05 → 7/20/05 |

### ASJC Scopus subject areas

- Signal Processing

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## Cite this

*2005 IEEE/SP 13th Workshop on Statistical Signal Processing - Book of Abstracts*(pp. 471-476). [1628641] (IEEE Workshop on Statistical Signal Processing Proceedings; Vol. 2005).