1 May 1990 Constrained sinogram restoration for limited-angle tomography
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Optical Engineering, 29(5), (1990). doi:10.1117/12.55622
Abstract
Tomographic reconstruction from incomplete data is required in many fields, including medical imaging, sonar, and radar. In this paper, we present a new reconstruction algorithm for limited-angle tomography, a problem that occurs when projections are missing over a range of angles. The approach uses a variational formulation that incorporates the Ludwig- Helgason consistency conditions, measurement noise statistics, and a sinogram smoothness condition. Optimal restored sinograms, therefore, satisfy an associated Euler-Lagrange partial differential equation, which we solve on a lattice using a primal-dual optimization procedure. Object estimates are then reconstructed using convolution backprojection applied to the restored sinogram. We present results of simulations that illustrate the performance of the algorithm and discuss directions for further research.
Jerry L. Prince, Alan S. Willsky, "Constrained sinogram restoration for limited-angle tomography," Optical Engineering 29(5), (1 May 1990). http://dx.doi.org/10.1117/12.55622
JOURNAL ARTICLE
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KEYWORDS
Tomography

Reconstruction algorithms

Radon transform

Convolution

Computer simulations

Partial differential equations

Signal to noise ratio

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