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    Area of Science:

    • Computer Vision
    • Image Processing
    • Optimization

    Background:

    • Image reconstruction relies on regularizers and loss functions within optimization frameworks.
    • Developing accurate and efficiently optimizable regularizers is a key challenge.

    Purpose of the Study:

    • To construct a novel quadratic regularizer for image reconstruction.
    • To achieve competitive reconstruction quality with efficient optimization.

    Main Methods:

    • Developed a quadratic regularizer with an objective function derived from observed data.
    • Utilized iterative Krylov solvers to reduce optimization to solving a linear system.
    • Incorporated forward operator and linear denoiser applications within solver iterations.

    Main Results:

    • The proposed quadratic regularizer demonstrates reconstruction capabilities competitive with state-of-the-art methods.
    • Optimization is reduced to solving a linear system, enabling efficient application in superresolution, deblurring, and inpainting.
    • Near state-of-the-art reconstruction quality was achieved using a linear solver.

    Conclusions:

    • The novel quadratic regularizer offers a powerful and efficient alternative for image reconstruction tasks.
    • The ability to achieve high-quality results with linear solvers is a significant advancement in the field.