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    We introduce Spherical Codes (SC) for diffusion MRI (dMRI) sampling, improving angular separation and rotational invariance over existing methods like Generalized EEM. This enhances data acquisition and reconstruction quality.

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    Area of Science:

    • Medical Imaging
    • Neuroscience
    • Computational Physics

    Background:

    • Diffusion MRI (dMRI) relies on effective sampling schemes for efficient data acquisition and accurate reconstruction.
    • Current methods like Generalized Electrostatic Energy Minimization (GEEM) are used but do not directly optimize for maximal angular separation between sampling points.

    Purpose of the Study:

    • To introduce a novel formulation, Spherical Code (SC), for designing optimal single and multi-shell dMRI sampling schemes.
    • To directly maximize the minimal angle between sampling points, enhancing rotational invariance and data quality.

    Main Methods:

    • Developed the Spherical Code (SC) formulation for continuous and discrete sampling problems in dMRI.
    • Proposed five algorithms: Incremental SC (ISC), Iterative Maximum Overlap Construction (IMOC), 1-Opt greedy, Mixed Integer Linear Programming (MILP), and Constrained Non-Linear Optimization (CNLO).
    • Applied SC to design and optimize sampling schemes for dMRI acquisition.

    Main Results:

    • SC methods achieved greater angular separation between sampling points compared to EEM and GEEM.
    • Demonstrated superior rotational invariance properties with SC-designed sampling schemes.
    • Experimental results validated the effectiveness of SC in improving dMRI sampling.

    Conclusions:

    • The Spherical Code formulation provides a more direct and effective approach to optimizing dMRI sampling schemes.
    • SC methods offer significant advantages in angular separation and rotational invariance over existing state-of-the-art techniques.
    • The developed algorithms and released codes (DMRITool) facilitate the practical application of SC in dMRI research.