Shape recovery for sparse‐data tomography

A two‐dimensional sparse‐data tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A nonuniform rational basis splines (NURBS) curve is used as a computational representation of the boundary. This approach conveniently provides the result in a f...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2017-12, Vol.40 (18), p.6649-6669
Main Authors: Haario, Heikki, Kallonen, Aki, Laine, Marko, Niemi, Esa, Purisha, Zenith, Siltanen, Samuli
Format: Article
Language:English
Subjects:
Attenuation coefficients
Bayesian analysis
CAD
Coefficient of variation
Computed tomography
Computer aided design
Computer simulation
Data recovery
Inverse problems
Markov analysis
Markov chains
Mathematical analysis
MCMC
Monte Carlo simulation
NURBS
Parameterization
Regularization
reverse engineering
shape recovery
Splines
Tomography
X‐ray tomography
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Summary:A two‐dimensional sparse‐data tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A nonuniform rational basis splines (NURBS) curve is used as a computational representation of the boundary. This approach conveniently provides the result in a format readily compatible with computer‐aided design software. However, the linear tomography task becomes a nonlinear inverse problem because of the NURBS‐based parameterization. Therefore, Bayesian inversion with Markov chain Monte Carlo sampling is used for calculating an estimate of the NURBS control points. The reconstruction method is tested with both simulated data and measured X‐ray projection data. The proposed method recovers the shape and the attenuation coefficient significantly better than the baseline algorithm (optimally thresholded total variation regularization), but at the cost of heavier computation.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4480