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Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
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    Area of Science:

    • Computer Vision
    • Geometric Processing
    • Image Denoising

    Background:

    • Total Generalized Variation (TGV) is effective for image processing, preserving sharp and smooth features.
    • Existing TGV methods are not suitable for 3D data, specifically triangular meshes.

    Purpose of the Study:

    • Develop a novel framework for discretizing second-order TGV on triangular meshes.
    • Propose a TGV-based variational method for denoising face normal fields on triangular meshes.

    Main Methods:

    • Developed a novel framework for discretizing second-order TGV on triangular meshes.
    • Proposed a TGV-based variational method with balanced first-order (sharp features) and second-order (smooth regions) terms.
    • Introduced an efficient iterative algorithm using variable-splitting and augmented Lagrangian for optimization.

    Main Results:

    • The proposed method effectively denoises face normal fields on triangular meshes.
    • Demonstrated superior performance over state-of-the-art methods on synthetic and real scanning data.
    • Achieved both visual and numerical improvements in denoising results.

    Conclusions:

    • The novel TGV discretization framework is suitable for 3D triangular meshes.
    • The proposed TGV-based denoising method preserves essential geometric features.
    • The method offers a significant advancement for 3D data processing and denoising.