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    This study re-establishes blind structured illumination microscopy (BSIM), highlighting pattern sparsity for super-resolution. Optimized illuminations and a faster reconstruction algorithm enhance resolving power for 3D and real-time 2D imaging.

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    Area of Science:

    • Microscopy and Imaging Technologies
    • Optical Physics
    • Computational Imaging

    Background:

    • Blind structured illumination microscopy (BSIM) offers super-resolution capabilities.
    • Understanding the fundamental mechanisms driving BSIM's resolution enhancement is crucial.

    Purpose of the Study:

    • To re-establish the theoretical foundation of BSIM, emphasizing the role of illumination pattern sparsity.
    • To explore methods for enhancing the resolving power of BSIM.
    • To develop an improved numerical algorithm for image reconstruction.

    Main Methods:

    • Theoretical re-foundation of the BSIM strategy.
    • Numerical analysis of optimized one-photon and two-photon speckle illuminations.
    • Development of a new preconditioned proximal iteration algorithm for image reconstruction under positivity constraints.

    Main Results:

    • The sparsity of illumination patterns is identified as central to BSIM's super-resolution mechanism.
    • Optimized speckle illuminations (one-photon and two-photon) can further enhance resolving power.
    • A significantly improved and faster numerical reconstruction algorithm is presented.

    Conclusions:

    • The findings provide a deeper theoretical understanding of BSIM.
    • The developed algorithm enables faster and potentially 3D and real-time 2D super-resolution imaging.
    • This work paves the way for advanced applications of structured illumination microscopy.