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Transient Optical Clearing Using Absorbing Molecules for Ex Vivo and In Vivo Imaging
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Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain.

Jiahao Pang, Gene Cheung

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |January 17, 2017
    PubMed
    Summary

    This study analyzes graph Laplacian regularization for image denoising by connecting it to Riemannian manifolds. An optimal regularizer is derived, improving denoising performance, especially for piecewise smooth images.

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    Area of Science:

    • Image processing
    • Computational mathematics
    • Computer vision

    Background:

    • Inverse imaging problems require regularization due to their underdetermined nature.
    • Graph Laplacian regularizers are popular but their underlying mechanisms are not fully understood.
    • Understanding these mechanisms is crucial for advancing image denoising techniques.

    Purpose of the Study:

    • To provide a deeper theoretical understanding of graph Laplacian regularization in image denoising.
    • To derive an optimal graph Laplacian regularizer by analyzing pixel patch neighborhoods as Riemannian manifolds.
    • To interpret graph Laplacian regularization as an anisotropic diffusion process.

    Main Methods:

    • Interpreting neighborhood graphs of pixel patches as discrete Riemannian manifolds.
    • Analyzing the convergence of the graph Laplacian regularizer to a continuous-domain functional.
    • Deriving an optimal metric space based on non-local self-similarity for denoising.
    • Developing an iterative image denoising algorithm based on the derived theoretical framework.

    Main Results:

    • Demonstrated convergence of the graph Laplacian regularizer to a continuous functional in a locally adaptive metric space.
    • Derived an optimal graph Laplacian regularizer by assuming non-local self-similarity in pixel patches.
    • Interpreted graph Laplacian regularization as an anisotropic diffusion scheme, explaining its behavior.
    • Developed a competitive iterative denoising algorithm.

    Conclusions:

    • The theoretical analysis provides fundamental insights into graph Laplacian regularization for image denoising.
    • The derived optimal regularizer enhances denoising performance, particularly for piecewise smooth images.
    • The proposed algorithm achieves competitive results compared to state-of-the-art methods like BM3D.