Constrained sinogram restoration for limited-angle tomography

Jerry Ladd Prince, Alan S. Willsky

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)535-544
Number of pages10
JournalOptical Engineering
Volume29
Issue number5
StatePublished - May 1990

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restoration
Restoration
Tomography
tomography
Reconstruction (structural)
sonar
Medical imaging
Sonar
noise measurement
Convolution
convolution integrals
partial differential equations
Partial differential equations
radar
Radar
projection
Statistics
statistics
formulations
optimization

ASJC Scopus subject areas

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

Cite this

Constrained sinogram restoration for limited-angle tomography. / Prince, Jerry Ladd; Willsky, Alan S.

In: Optical Engineering, Vol. 29, No. 5, 05.1990, p. 535-544.

Research output: Contribution to journalArticle

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