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Characteristic functionals in imaging and image-quality assessment: tutorial.

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    Characteristic functionals quantify random fields in imaging systems. These methods enable parameter estimation, object classification, and image quality assessment for improved imaging system performance.

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    Area of Science:

    • * Mathematical imaging science
    • * Statistical signal processing
    • * Random field theory

    Background:

    • * Random fields are essential for modeling ensembles of objects in imaging systems.
    • * Characteristic functionals provide analytical tools for quantifying statistical properties of random fields.
    • * Modern digital imaging systems require methods applicable to finite-dimensional data.

    Purpose of the Study:

    • * To introduce the theory and applications of characteristic functionals in imaging.
    • * To discuss the propagation of characteristic functionals through imaging systems.
    • * To present methods for parameter estimation, object classification, and image quality assessment.

    Main Methods:

    • * Introduction to the general theory of characteristic functionals.
    • * Analysis of characteristic functional propagation in binned and list-mode imaging systems.
    • * Application of maximum likelihood and maximum a posteriori techniques in functional spaces.
    • * Calculation of the Fisher information matrix in the context of characteristic functionals.

    Main Results:

    • * Demonstrated methods for estimating population parameters from image data using characteristic functionals.
    • * Developed classifiers for populations of objects based on characteristic functionals and imaging data.
    • * Showed how to compute the Fisher information matrix in the relevant functional space.
    • * Established the utility of these methods for image quality assessment.

    Conclusions:

    • * Characteristic functionals are powerful tools for analyzing random fields in imaging.
    • * The presented methods facilitate parameter estimation, classification, and image quality assessment.
    • * This framework enhances the understanding and evaluation of imaging systems.