The image restoration of single-pixel imaging relies on the connection between the received signal and the modulated light source, including computational ghost imaging and compressed sensing imaging. Computational ghost imaging uses a high-order intensity correlation function between the light source and the single-pixel signal to restore the image, while compressed sensing imaging uses an optimized compressed sensing algorithm to restore the image. Typically, single-pixel imaging experiments use a wide variety of light sources, including physical light sources, such as thermal light, X-rays, electrons, neutrons, and single photon sources, and artificial light sources modulated by spatial light modulators and digital micromirror systems. These light sources follow different statistical probability distributions, and the light field intensity of the illuminated object can be considered as a statistically independent continuous or discrete random variable, also known as a reference signal. The single-pixel signal is a linear combination of all reference signals. The joint statistical probability distribution between the reference signal and the single pixel signal is determined according to the statistical properties of the light source. In addition, we investigate the effects of the probability distribution functions on the image quality, providing theoretical bases of physics and statistics for single-pixel imaging.