Recovering convex boundaries from blurred and noisy observations
| dc.creator | Goldenshluger, Alexander | |
| dc.creator | Zeevi, Assaf | |
| dc.date | 2006-08-01 | |
| dc.date.accessioned | 2026-07-07T08:08:04Z | |
| dc.date.available | 2026-07-07T08:08:04Z | |
| dc.description | 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. | |
| dc.description | Published at http://dx.doi.org/10.1214/009053606000000326 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0608012 | |
| dc.identifier | http://arxiv.org/abs/math/0608012 | |
| dc.identifier | Annals of Statistics 2006, Vol. 34, No. 3, 1375-1394 | |
| dc.identifier | doi:10.1214/009053606000000326 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131135 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G05, 62H35 (Primary) | |
| dc.title | Recovering convex boundaries from blurred and noisy observations | |
| dc.type | text |