Assaf Zeevi

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
Exact Citation:
Goldenshluger, Alexander, and Assaf Zeevi. "Recovering convex boundaries from blurred and noisy observations." The Annals of Statistics 34, no. 3 (June 2006): 1375-1394.
Volume: 34
Number: 3
Pages: 1375-1394
Date: 6 2006