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    Area of Science:

    • Data Science
    • Machine Learning
    • Image Analysis

    Background:

    • Transport-based techniques are gaining traction for signal and data analysis.
    • These methods excel at creating accurate generative models for data distributions.
    • Their geometric properties inspire novel data interpretation algorithms.

    Purpose of the Study:

    • To provide a practical overview of mass transport methods.
    • To cover the mathematical underpinnings and numerical implementation.
    • To review and demonstrate various applications of these techniques.

    Main Methods:

    • Exploration of mathematical foundations of mass transport.
    • Discussion of numerical implementation strategies.
    • Review of diverse applications with demonstrations.

    Main Results:

    • Demonstrated state-of-the-art results in multiple applications.
    • Highlighted the utility in content-based retrieval, cancer detection, and image super-resolution.
    • Showcased the effectiveness of transport-related metrics for data interpretation.

    Conclusions:

    • Mass transport methods are powerful tools for signal and data analysis.
    • These techniques offer significant advantages in various scientific and technical fields.
    • Accessible software is provided to facilitate practical implementation and further research.