Recovering convex edges of an image from noisy tomographic data

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 deve...

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Bibliographic Details
Published in:IEEE transactions on information theory 2006-04, Vol.52 (4), p.1322-1334
Main Authors: Goldenshluger, A., Spokoiny, V.
Format: Article
Language:English
Subjects:
Applied sciences
Biomedical equipment
Body regions
Boundaries
Convergence
Data analysis
Discontinuity
Edge detection
Estimating techniques
Estimators
Exact sciences and technology
Image edge detection
Image reconstruction
Information, signal and communications theory
Mathematical analysis
Mathematics
Medical services
minimax estimation
Minimax techniques
Miscellaneous
optimal rates of convergence
Optimization
Pattern recognition
Radon transform
Recovering
Shape
Signal processing
support function
Telecommunications and information theory
Tomography
Transforms
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Summary: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.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2006.871053