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On the Iterative Image Space Reconstruction Algorthm for ECT.

D M Titterington

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    The Iterative Singular-value Ratio Algorithm (ISRA) converges to positive least-squares estimates for emission densities. However, these estimators are asymptotically inferior to maximum likelihood estimators, as shown by simple examples.

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    Area of Science:

    • Statistical modeling
    • Signal processing

    Background:

    • Iterative Singular-value Ratio Algorithm (ISRA) is used for estimating emission densities.
    • Understanding the convergence properties and limitations of ISRA is crucial for its application.

    Purpose of the Study:

    • To analyze the convergence of the ISRA algorithm.
    • To compare ISRA with maximum likelihood estimators (MLEs).
    • To identify potential behavioral issues of ISRA.

    Main Methods:

    • Convergence analysis of the ISRA algorithm.
    • Asymptotic theory comparison with MLEs.
    • Illustrative examples to demonstrate algorithm behavior.

    Main Results:

    • ISRA converges to elementwise strictly positive least-squares estimates when a unique solution exists.
    • ISRA estimators are asymptotically inferior to MLEs.
    • Simple examples highlight potential difficulties with ISRA's behavior.

    Conclusions:

    • ISRA provides a method for estimating positive emission densities.
    • MLEs, computationally facilitated by the EM algorithm, offer superior asymptotic properties.
    • Careful consideration of ISRA's limitations is advised.