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    Area of Science:

    • Tomographic Imaging
    • Computational Imaging
    • Image Reconstruction

    Background:

    • Dynamic reconstruction is crucial in applications like medical imaging and process tomography.
    • Kalman filters are common but suffer from tuning difficulties and rely on simplified models.
    • Existing methods struggle with complex geometric deformations.

    Purpose of the Study:

    • To develop a novel reconstruction scheme for ray tomography that minimizes filter tuning issues.
    • To accurately reconstruct time-varying, geometrically deforming features.
    • To handle affine and pointwise-normal scaling motions in tomographic imaging.

    Main Methods:

    • A level-set-based reconstruction scheme for ray tomography is proposed.
    • A regularized Gauss-Newton-filter-based approach is utilized.
    • Implicit Hermite-interpolation-based radial basis functions represent the boundary curve.
    • Shape-related Frechet derivatives are evaluated without needing the pointwise Jacobian.

    Main Results:

    • The proposed method successfully reconstructs shape and electromagnetic parameters in dynamic ray tomography.
    • Numerical results validate the formulation for straight ray-based tomographic reconstruction.
    • The scheme effectively handles affine and pointwise-normal scaling motions.

    Conclusions:

    • The novel level-set method offers an effective solution for dynamic tomographic reconstruction challenges.
    • This work presents the first tomographic reconstruction results for these specific settings.
    • The approach minimizes tuning issues and improves accuracy for deforming features.