An Adaptive Sampling Fourier Single-Pixel Imaging Method Based on Discrete Coefficients

Guangyao Chen, Yuanping Xu, Jiliu Zhou, Zhijie Xu, Chaolong Zhang, Chao Kong, Tukun Li, Qiuyan Gai

Abstract: Fourier Single-Pixel Imaging (FSPI) can directly obtain the Fourier spectrum of a target scene and reconstruct it. However, the existing FSPI spectrum sampling methods are mostly constrained within a prior range, which makes it challenging to balance the image details and noise suppression under limited samples and short reconstruction time. One of the crucial issues in the practical application of SPI technology is how to enhance its imaging speed while ensuring the quality of the imaging. Therefore, this study proposed an adaptive sampling FSPI method based on discrete coefficients. This method utilizes the characteristic of energy concentration in the Fourier spectrum to plan circular and rectangular sampling paths in the frequency domain. Measurements are taken along the planned sampling paths, and the mean and standard deviation of each segment are calculated to obtain the discrete coefficients. When the discrete coefficient exceeds the threshold, the sampling stops automatically. Then, the target image is reconstructed by performing the inverse Fourier transform on the acquired spectrum. The method proposed in this article has significantly improved the imaging efficiency of SPI.