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    Area of Science:

    • Image processing
    • Computational imaging
    • Signal processing

    Background:

    • Photon-counting sensors produce images with inherent Poisson noise.
    • Total Variation (TV) regularization is effective for image deconvolution but has limitations in preserving local image details and can cause staircase artifacts.
    • Existing nonlocal methods struggle to adapt to varying image intensities and maintain fine details.

    Purpose of the Study:

    • To develop an advanced image deconvolution technique that overcomes the limitations of traditional Total Variation (TV) regularization.
    • To introduce an intensity-adaptive nonlocal regularization model for improved detail preservation in noisy images.
    • To propose a hybrid regularization approach combining nonlocal features with high-order derivative sparsity to mitigate staircase effects.

    Main Methods:

    • Extended global Total Variation (TV) to nonlocal modeling using an intensity-adaptive nonlocal regularization based on similar image blocks.
    • Developed a hybrid nonlocal regularization by incorporating the sparsity of high-order derivatives to address staircase artifacts.
    • Employed an efficient alternating direction method of multipliers (ADMM) algorithm for model optimization.
    • Investigated and analyzed adaptive strategies for selecting regularization parameters.

    Main Results:

    • The proposed hybrid high-order nonlocal gradient sparsity regularization model significantly reduces computational time compared to existing nonlocal restoration algorithms.
    • The method effectively preserves image details and mitigates staircase artifacts, leading to clearer and more accurate image recovery.
    • Experimental results demonstrate superior performance in terms of both image quality and computational efficiency.

    Conclusions:

    • The developed hybrid regularization model offers a significant advancement in Poisson noise deconvolution for photon-counting sensor images.
    • The intensity-adaptive nonlocal approach combined with high-order sparsity effectively balances detail preservation and artifact reduction.
    • This method provides a computationally efficient and high-quality solution for image restoration tasks in scientific imaging.