Recovering convex edges of an image from noisy tomographic data

Author

Goldenshluger, Alexander ; Spokoiny, Vladimir

Author_Institution

Dept. of Stat., Haifa Univ., Israel

Volume

52

Issue

4

fYear

2006

fDate

4/1/2006 12:00:00 AM

Firstpage

1322

Lastpage

1334

Abstract

We consider the problem of recovering edges of an image from noisy tomographic data. The original image is assumed to have a discontinuity jump (edge) along the boundary of a compact convex set. The Radon transform of the image is observed with noise, and the problem is to estimate the edge. We develop an estimation procedure which is based on recovering the support function of the edge. It is shown that the proposed estimator is nearly optimal in order in a minimax sense. Numerical examples illustrate reasonable practical behavior of the estimation procedure.

Keywords

Radon transforms; edge detection; image denoising; image reconstruction; minimax techniques; tomography; Radon transform; convex edge recovery; image reconstruction; minimax estimation; noisy tomographic data; Biomedical equipment; Body regions; Convergence; Image edge detection; Image reconstruction; Mathematics; Medical services; Minimax techniques; Shape; Tomography; Edge detection; Radon transform; minimax estimation; optimal rates of convergence; support function;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2006.871053

Filename

1614068