A new framework for sparse regularization in limited angle x-ray tomography

  • Authors:

  • Jürgen Frikel

  • Affiliations:

  • Image Diagnost International GmbH, München, Germany and M6 - Mathematische Modellbildung, Technische Universität München, Zentrum Mathematik, München, Germany

  • Venue:
  • ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
  • Year:
  • 2010

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Abstract

We propose a new framework for limited angle tomographic reconstruction. Our approach is based on the observation that for a given acquisition geometry only a few (visible) structures of the object can be reconstructed reliably using a limited angle data set. By formulating this problem in the curvelet domain, we can characterize those curvelet coefficients which correspond to visible structures in the image domain. The integration of this infonnation into the formulation of the reconstruction problem leads to a considerable dimensionality reduction and yields a speedup of the corresponding reconstruction algorithms.