Efficient single pixel imaging in Fourier space

Abstract

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