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    We introduce novel frequency domain edge detection methods using single-pixel imaging. SCHEME-I enhances signal-to-noise ratio for high-frequency components, improving edge detection quality for objects and characters.

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    Area of Science:

    • Optics
    • Image Processing
    • Computational Imaging

    Background:

    • Edge detection is crucial for image analysis.
    • Traditional methods face limitations in complex imaging scenarios.
    • Single-pixel imaging offers unique advantages for indirect measurements.

    Purpose of the Study:

    • To propose and validate new frequency domain edge detection schemes.
    • To leverage single-pixel imaging for enhanced edge reconstruction.
    • To improve signal-to-noise ratio in edge detection algorithms.

    Main Methods:

    • Development of two schemes (SCHEME-I and SCHEME-II) for frequency domain edge detection.
    • Utilizing sinusoidal patterns and four-step phase-shifting in SCHEME-I.
    • Employing Fourier transforms and inverse Fourier transforms for edge reconstruction.
    • Experimental and numerical simulation validation.

    Main Results:

    • Both schemes successfully reconstruct edges of character and image objects.
    • SCHEME-I demonstrates superior signal-to-noise ratio for high-frequency components compared to SCHEME-II.
    • SCHEME-I shows improved signal-to-noise ratio over speckle-shifting ghost imaging edge detection.
    • Effective reduction in measurement requirements due to Fourier domain sparsity.

    Conclusions:

    • The proposed frequency domain edge detection schemes are effective.
    • SCHEME-I offers significant advantages in signal-to-noise ratio and experimental results.
    • Single-pixel imaging enables robust edge reconstruction from indirect measurements.