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    Area of Science:

    • Microscopy and Imaging Science
    • Optical Physics
    • Signal Processing

    Background:

    • Compressive imaging (CI) offers enhanced spatial resolution beyond the Abbe diffraction limit.
    • CI reconstructs high-resolution images from fewer measurements than pixels, overcoming the Nyquist limit.
    • Sparsity constraints are crucial for effective CI reconstruction.

    Purpose of the Study:

    • To determine the fundamental resolution limits of noiseless compressive imaging.
    • To analyze the impact of speckle illumination and single-pixel detection on resolution.
    • To investigate the role of discretization and the effect of oversampling.

    Main Methods:

    • Theoretical analysis of compressive imaging systems.
    • Numerical simulations of image reconstruction.
    • Utilized randomly generated speckle patterns via scattering media or multimode fiber.

    Main Results:

    • Demonstrated the optimal number of measurements required for high-resolution imaging.
    • Identified the ultimate spatial resolution limits achievable with this technique.
    • Highlighted the significant impact of discretization on image quality and resolution.

    Conclusions:

    • Oversampling in compressive imaging can decrease resolution and reconstruction quality, contrary to conventional microscopy.
    • Understanding discretization is vital for optimizing compressive imaging performance.
    • This work provides fundamental insights into the limits and optimal design of sparsity-constrained compressive imaging systems.