Constrained sinogram restoration for limited-angle tomography

Jerry L. Prince, Alan S. Willsky

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)535-544
Number of pages10
JournalOptical Engineering
Issue number5
StatePublished - 1990

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Engineering(all)


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