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June 2006 Recovering convex boundaries from blurred and noisy observations
Alexander Goldenshluger, Assaf Zeevi
Ann. Statist. 34(3): 1375-1394 (June 2006). DOI: 10.1214/009053606000000326


We consider the problem of estimating convex boundaries from blurred and noisy observations. In our model, the convolution of an intensity function f is observed with additive Gaussian white noise. The function f is assumed to have convex support G whose boundary is to be recovered. Rather than directly estimating the intensity function, we develop a procedure which is based on estimating the support function of the set G. This approach is closely related to the method of geometric hyperplane probing, a well-known technique in computer vision applications. We establish bounds that reveal how the estimation accuracy depends on the ill-posedness of the convolution operator and the behavior of the intensity function near the boundary.


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Alexander Goldenshluger. Assaf Zeevi. "Recovering convex boundaries from blurred and noisy observations." Ann. Statist. 34 (3) 1375 - 1394, June 2006.


Published: June 2006
First available in Project Euclid: 10 July 2006

zbMATH: 1113.62116
MathSciNet: MR2278361
Digital Object Identifier: 10.1214/009053606000000326

Primary: 62G05 , 62H35

Keywords: boundary estimation , convex sets , Deconvolution , geometric probing , image analysis , rates of convergence , support function

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 3 • June 2006
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