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    Iterative phase retrieval often faces the twin image problem. Introducing a sparsity-enhancing step effectively solves this issue for complex-valued objects, even with centrosymmetric support.

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    Area of Science:

    • Optics and Photonics
    • Image Processing
    • Computational Imaging

    Background:

    • Iterative phase retrieval from Fourier magnitude data is crucial for reconstructing complex-valued objects.
    • A significant challenge is the 'twin image problem,' where solutions contain artifacts.
    • This problem is exacerbated by centrosymmetric object support, leading to algorithm stagnation.

    Purpose of the Study:

    • To address the twin image problem in iterative phase retrieval.
    • To develop a method that enhances sparsity to overcome solution stagnation.
    • To validate the approach for complex-valued objects, including those with centrosymmetric support.

    Main Methods:

    • Introducing a sparsity-enhancing step into iterative phase retrieval algorithms.
    • Leveraging the observation that ideal solutions are sparser in transform domains.
    • Testing the method on binary and gray-scale pure phase objects in simulations.

    Main Results:

    • The proposed sparsity-enhancing step effectively mitigates the twin image problem.
    • The algorithm successfully recovers the desired phase image without its twin replica.
    • The method remains effective even when the object support is centrosymmetric.

    Conclusions:

    • Sparsity-assisted iterative phase retrieval offers a robust solution to the twin image problem.
    • This approach enhances the accuracy and reliability of phase reconstruction.
    • The technique is particularly valuable for complex-valued objects with challenging support symmetries.