Constrained sinogram restoration for limited-angle tomography

Jerry L. Prince; Alan S. Willsky

doi:10.1117/12.55622

1 May 1990 Constrained sinogram restoration for limited-angle tomography

Jerry L. Prince, Alan S. Willsky

Author Affiliations +

Optical Engineering, Vol. 29, Issue 5, (May 1990). https://doi.org/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.

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Jerry L. Prince and Alan S. Willsky "Constrained sinogram restoration for limited-angle tomography," Optical Engineering 29(5), (1 May 1990). https://doi.org/10.1117/12.55622

Published: 1 May 1990

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