Recovering convex boundaries from blurred and noisy observations
Coauthor(s): Alexander Goldenshluger.
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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.
Source: The Annals of Statistics
Goldenshluger, Alexander, and Assaf Zeevi. "Recovering convex boundaries from blurred and noisy observations." The Annals of Statistics 34, no. 3 (June 2006): 1375-1394.