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Tomographic reconstruction from limited angular data.

A Peres

    Journal of Computer Assisted Tomography
    |December 1, 1979
    PubMed
    Summary
    This summary is machine-generated.

    Reconstructing a complete shadow from limited projection data is possible using trigonometric polynomials. However, this method

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    Area of Science:

    • Mathematical imaging and data analysis.
    • Tomographic reconstruction principles.

    Background:

    • Projection measurements (Mn(phi)) are fundamental in various imaging techniques.
    • The nth moment of a projection is theoretically a trigonometric polynomial of degree n.

    Purpose of the Study:

    • To explore the theoretical reconstruction of a complete shadow from limited projection data.
    • To assess the practical limitations of such reconstruction algorithms.

    Main Methods:

    • Utilizing the property that the nth moment of a projection (Mn(phi)) is a trigonometric polynomial.
    • Measuring projection moments at n+1 discrete angles (phi i) to reconstruct the full moment function Mn(phi).

    Main Results:

    • Demonstrated that Mn(phi) can be reconstructed from discrete measurements.

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  • Identified that the reconstruction algorithm is straightforward in principle.
  • Highlighted severe limitations due to data noise.

    • Conclusions:

    • Theoretical reconstruction of a complete shadow is feasible from limited angular data.
    • Practical application is significantly hindered by noise sensitivity in projection measurements.