Efficient single pixel imaging in Fourier space

Single pixel imaging (SPI) is a novel technique being able to capture 2D images using a bucket detector with high signal-to-noise ratio, wide spectrum range and low cost. Conventional SPI projects random illumination patterns to randomly and uniformly sample the entire scene's information. Determined by the Nyquist sampling theory, SPI needs either numerous projections or high computation cost to reconstruct the target scene, especially for high-resolution cases. To address this issue, we propose an efficient single pixel imaging technique (eSPI), which instead projects sinusoidal patterns for importance sampling of the target scene's spatial spectrum in Fourier space. Specifically, utilizing the centrosymmetric conjugation and sparsity priors of natural images' spatial spectra, eSPI sequentially projects two $\frac{\pi}{2}$-phase-shifted sinusoidal patterns to obtain each Fourier coefficient in the most informative spatial frequency bands. eSPI can reduce requisite patterns by two orders of magnitude compared to conventional SPI, which helps a lot for fast and high-resolution SPI.