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Minimum risk wavelet shrinkage operator for Poisson image denoising.

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    This study introduces new shrinkage operators for Skellam distribution to minimize errors in multiscale Poisson image denoising. The developed method effectively reduces noise, enhancing image quality with minimal L2 error.

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    Area of Science:

    • Digital Image Processing
    • Computational Imaging
    • Signal Processing

    Background:

    • Image sensors often capture data corrupted by Poisson noise.
    • Existing multiscale Poisson image denoising methods utilize Haar frame and wavelet coefficients, modeled using Skellam distribution.
    • Previous techniques focused on modeling coefficients rather than optimizing denoising operators.

    Purpose of the Study:

    • To develop novel shrinkage operators for the Skellam distribution tailored for multiscale Poisson image denoising.
    • To minimize the risk functional in the context of Poisson image denoising.
    • To achieve denoised wavelet coefficients with the minimum attainable L2 error.

    Main Methods:

    • Analysis of Skellam distribution for modeling wavelet and Haar frame coefficients.
    • Derivation and solving of shrinkage operators that minimize a defined risk functional.
    • Application of the derived minimum risk shrinkage operators to Poisson noisy images.

    Main Results:

    • Successfully derived shrinkage operators for Skellam distribution that minimize the risk functional.
    • Demonstrated that the minimum risk shrinkage operator yields denoised wavelet coefficients with minimal L2 error.
    • The proposed method offers an improvement over existing techniques in terms of error minimization.

    Conclusions:

    • The developed minimum risk shrinkage operator is effective for multiscale Poisson image denoising.
    • This approach provides a mathematically rigorous way to minimize L2 error in denoised coefficients.
    • The findings contribute to advancing the field of image denoising, particularly for Poisson noise corrupted images.