Suppressing the noise in binarized Fourier single-pixel imaging utilizing defocus blur

Sinusoidal Fourier patterns are one of the orthogonal basis patterns used in single-pixel imaging. By retrieving the complex Fourier coefficients with phase-shifting algorithm, it reconstructs the image of a scene using inverse Fourier transform. It has been shown that Fourier single-pixel imaging is particularly well-suited to non conventional imaging applications. However, the frame rate of Fourier single-pixel imaging system is limited because the Fourier patterns are grayscale while the digital micromirror device performs binary modulation much faster than grayscale modulation. The fast Fourier single-pixel imaging addressed the problem by binarizing the patterns, however, the quality of the reconstructed image is jeopardized by the extra induced noise. Here we proposed to suppress the binarization induced noise while keeping the high-speed merit by deliberately applying a precomputed defocus. Numerical simulation and experimental results showed that the proposed method reconstructed images with an averaged 12% lower root mean squared error and similar to 90% higher signal-to-noise ratio than the fast Fourier method did. To some extent, the proposed method overcame the limitation of the quality-speed trade-off in Fourier single-pixel imaging and made both low noise and high frame rate available simultaneously.