Application of a Discrete Tomography Approach to Computerized Tomography

  • Y. Gerard
  • F. Feschet
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


Linear programming is used in discrete tomography to solve the relaxed problem of reconstructing a function f with values in the interval [0,1]. The linear program minimizes the uniform norm Ax - 6∞ or the 1-norm ∞∞Ax - b∞∞1 of the error on the projections. We can add to this objective function a linear penalty function p(x) for trying to obtain smooth solutions. The same approach can be used in computerized tomography. The question is if it can provide better images than the classical methods of computerized tomography. The aim of this chapter is to provide a tentative answer. We present a preliminary study on real acquisitions from a phantom and provide reconstructions from a few projections, with qualities similar to the traditional methods.


Single Photon Emission Compute Tomography Gray Level Interior Point Method Order Subset Expectation Maximization Algebraic Reconstruction Technique 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Birkhäuser Boston 2007

Authors and Affiliations

  • Y. Gerard
    • 1
  • F. Feschet
    • 1
  1. 1.University of Auvergne 1 - IUT/LAIC LaboratoryAubiere CedexFrance

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