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Three-Dimensional Phase Resolved Functional Lung Magnetic Resonance Imaging
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Bandwidth-optimized regularization for low-frequency recovery in quantitative phase imaging.

Alejandro Silva, Julia Alonso

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    |April 24, 2026
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    Summary
    This summary is machine-generated.

    We introduce an improved matrix solution for the transport of intensity equation (EMS-TIE) with a tunable parameter. This method enhances signal recovery and phase retrieval accuracy compared to standard Tikhonov techniques.

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    Area of Science:

    • Optical imaging
    • Computational optics
    • Image reconstruction

    Background:

    • The transport of intensity equation (TIE) is crucial for phase retrieval in optical microscopy.
    • Conventional Tikhonov regularization methods for TIE have limitations due to coupled filter bandwidth and cutoff frequency.
    • Optimizing signal recovery and phase information in TIE remains a challenge.

    Purpose of the Study:

    • To propose an enhanced matrix solution for the transport of intensity equation (EMS-TIE).
    • To introduce a tunable parameter (th) in the Tikhonov regularization term for improved performance.
    • To overcome the limitations of conventional Tikhonov solvers in TIE.

    Main Methods:

    • Development of the expanded matrix solution of the transport of intensity equation (EMS-TIE).
    • Incorporation of a tunable parameter (th) into the Tikhonov regularization.
    • Decoupling of filter bandwidth and cutoff frequency for enhanced control.
    • Simulations and experimental validation of the proposed method.

    Main Results:

    • The EMS-TIE with a tunable parameter allows for optimized filter shape tuning.
    • Increasing the passband width significantly reduces retrieval error.
    • Enhanced low-frequency phase recovery is achieved compared to standard methods.
    • The proposed method outperforms standard Tikhonov-based approaches.

    Conclusions:

    • The EMS-TIE offers a flexible and effective approach for phase retrieval.
    • Tunable regularization parameters improve the accuracy and robustness of TIE solvers.
    • This method provides a significant advancement for quantitative phase imaging applications.