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No Access Submitted: 05 February 2002 Accepted: 21 March 2002 Published Online: 21 June 2002

  • Reconstruction of Abel-transformable images: The Gaussian basis-set expansion Abel transform method

Review of Scientific Instruments 73, 2634 (2002); https://doi.org/10.1063/1.1482156
Vladimir Dribinski
  • Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
    • Alexei Ossadtchi
  • Signal and Image Processing Institute, Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089
    • Vladimir A. Mandelshtam
  • Department of Chemistry, University of California at Irvine, Irvine, California 92697
    • Hanna Reisler
  • Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
    • more...View Contributors
    • Vladimir Dribinski
    • Alexei Ossadtchi
    • Vladimir A. Mandelshtam
    • Hanna Reisler
    ABSTRACT
    In this article we present a new method for reconstructing three-dimensional (3D) images with cylindrical symmetry from their two-dimensional projections. The method is based on expanding the projection in a basis set of functions that are analytical projections of known well-behaved functions. The original 3D image can then be reconstructed as a linear combination of these well-behaved functions, which have a Gaussian-like shape, with the same expansion coefficients as the projection. In the process of finding the expansion coefficients, regularization is used to achieve a more reliable reconstruction of noisy projections. The method is efficient and computationally cheap and is particularly well suited for transforming projections obtained in photoion and photoelectron imaging experiments. It can be used for any image with cylindrical symmetry, requires minimal user’s input, and provides a reliable reconstruction in certain cases when the commonly used Fourier–Hankel Abel transform method fails.

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    1. © 2002 American Institute of Physics.

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