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    This study introduces a novel low-rank approximation for the non-local means (NLM) operator, enhancing image denoising. The improved NLM method reduces noise sensitivity while preserving image details effectively.

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    Area of Science:

    • Image processing
    • Computational mathematics

    Background:

    • Non-local means (NLM) is a powerful image denoising technique.
    • NLM can be computationally intensive and sensitive to noise.

    Purpose of the Study:

    • To develop an efficient and noise-robust NLM operator.
    • To improve the performance of NLM for natural image denoising.

    Main Methods:

    • Low-rank approximation of the NLM operator using spectral filtering.
    • Efficient implementation via Chebyshev polynomials.
    • Application to natural image denoising with comparative analysis.

    Main Results:

    • The proposed low-rank NLM operator demonstrates reduced sensitivity to noise.
    • Important properties of the original NLM operator are preserved.
    • Effective denoising performance on natural images compared to existing methods.

    Conclusions:

    • The low-rank approximation offers a significant improvement for NLM-based image denoising.
    • The method provides a computationally efficient and robust alternative for noise reduction.