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Generalized proximal smoothing (GPS) for phase retrieval.

Minh Pham, Penghang Yin, Arjun Rana

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    Summary
    This summary is machine-generated.

    We developed a new generalized proximal smoothing (GPS) algorithm for phase retrieval from noisy data. GPS demonstrates superior convergence, consistency, and noise robustness compared to traditional methods like HIO and OSS.

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    Area of Science:

    • Computational imaging
    • Signal processing
    • Optimization algorithms

    Background:

    • Phase retrieval is crucial in many imaging applications.
    • Classical algorithms struggle with noisy data and convergence.
    • Existing methods often lack robustness to noise and exhibit slow convergence.

    Purpose of the Study:

    • To introduce the generalized proximal smoothing (GPS) algorithm for robust phase retrieval.
    • To address limitations of existing phase retrieval techniques, particularly in noisy conditions.
    • To enhance convergence speed and consistency in phase retrieval.

    Main Methods:

    • Developed the generalized proximal smoothing (GPS) algorithm, an optimization-based approach.
    • Incorporated Moreau-Yosida regularization and heat kernel smoothing to relax support constraints.
    • Relaxed magnitude constraints using a least squares fidelity term.
    • Utilized iterative proximal mappings in primal and dual spaces.

    Main Results:

    • GPS algorithm shows improved convergence speed over HIO and OSS.
    • Demonstrated enhanced consistency in phase retrieval results.
    • Exhibited superior robustness to noise in both simulations and experimental data.
    • GPS consistently outperformed classical phase retrieval algorithms.

    Conclusions:

    • The GPS algorithm offers a significant advancement for phase retrieval from noisy data.
    • GPS provides a more reliable and efficient solution compared to existing methods.
    • The developed algorithm enhances the practical applicability of phase retrieval in various scientific fields.