Fourier single-pixel imaging based on diffusion models and composite random spectral sampling

To address the severe loss of high-frequency information in traditional Fourier Single-Pixel Imaging (FSPI) under extremely low sampling rates, this study proposes a diffusion model reconstruction method based on Gaussian random sampling and a centrosymmetric low-frequency enhancement strategy. In contrast to conventional uniform or lowfrequency square sampling strategies, the proposed method is characterized by the use of Gaussian random distribution sampling to increase the detection probability of high-frequency components, while enhanced sampling in the central region is employed to preserve the integrity of low-frequency information. This approach creates a data acquisition pattern that better aligns with the spectral characteristics of natural images. Subsequently, a diffusion generative model is constructed, integrating the composite spectrum derived from physical sampling as a consistency constraint and utilizing data priors to guide the iterative reconstruction process. Experimental results demonstrate that the proposed method achieves high-quality image reconstruction even at extremely low sampling rates (e.g., 5%), outperforming traditional methods in both subjective visual perception and quantitative metrics. This study offers a new perspective for the application of FSPI technology under low sampling conditions, further enhancing its practicality and adaptability.