SSP'05 -- Proceedings

	IEEE/SP 13th workshop on Statistical Signal Processing July, 17-20, 2005 - Bordeaux - France

Information regarding the paper

Title

Asymptotic Global Confidence Regions for 3-D Parametric Shape Estimation in Inverse Problems

Author(s)

Jong Ye	KAIST, Korea
PIerre Moulin	University of Illinois
Yoram Bresler	University of Illinois

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Abstract

This paper derives fundamental performance bounds for estimating 3-D parametric surface in inverse problems. Unlike conventional pixel-based image reconstruction problems, 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 the geometric inference and optimization of the imaging systems. However, compared to two-dimensional global confidence region analysis, computation of the probability that the entire 3-D surface estimate lies within the confidence region is much challenging problem since a surface estimate is an inhomogeneous random field continuously indexed by a two-dimensional index set. We derive lower bounds on this probability using the so-called tube formula for the tail probability of Gaussian random fields. Simulation results demonstrate the tightness of the bounds and the usefulness of 3-D global confidence region approaches.