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Recovering convex boundaries from blurred and noisy observations

Alexander Goldenshluger·Assaf Zeevi
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Abstract

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. 2006-08-01. Recovering convex boundaries from blurred and noisy observations. https://doi.org/10.1214/009053606000000326

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