Asymptotic global confidence regions for 3-D parametric shape estimation in inverse problems

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publication2005 IEEE/SP 13th Workshop on Statistical Signal Processing - Book of Abstracts
Pages471-476
Number of pages6
StatePublished - Dec 1 2005
Event2005 IEEE/SP 13th Workshop on Statistical Signal Processing - Bordeaux, France
Duration: Jul 17 2005Jul 20 2005

Publication series

NameIEEE Workshop on Statistical Signal Processing Proceedings
Volume2005

Other

Other2005 IEEE/SP 13th Workshop on Statistical Signal Processing
CountryFrance
CityBordeaux
Period7/17/057/20/05

ASJC Scopus subject areas

  • Signal Processing

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  • Cite this

    Ye, J. C., Moulin, P., & Bresler, Y. (2005). Asymptotic global confidence regions for 3-D parametric shape estimation in inverse problems. In 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).