Extremely undersampled fourier single-pixel imaging via trajectory- and measurement constrained diffusion framework

Extremely undersampled Fourier single-pixel imaging (FSPI) suffers from severe loss of structural details and reconstruction fidelity because only a limited number of low-frequency Fourier coefficients can be acquired. To address this challenge, we propose a diffusion reconstruction framework under trajectory and measurement constraints for extremely undersampled FSPI. The inverse Fourier reconstruction of the acquired low-frequency coefficients provides an observation-dependent mean, the maximum-likelihood trajectory objective inherited from the image restoration stochastic differential equation (IR-SDE) framework stabilizes the reverse recovery path, and progressive Fourier-domain measurement consistency repeatedly anchors reconstruction to the acquired spectrum. Experiments on animal and coin datasets show that the proposed method achieves higher average peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) than conventional FSPI, U-Net, IR-SDE, and NCSN++ at the sampling rates of 1 %, 3 %, and 5 %. On the simulated coin dataset, it achieves a 1.97 dB PSNR improvement over IR-SDE at the sampling rate of 1 %. Compared with the 1500-step predictor–corrector NCSN++ baseline, the 100-step proposed method reduces the average reconstruction time from 29.56 s to 1.09 s per 128 × 128-pixel image under the same hardware setting, providing a favorable balance between reconstruction quality and computational time and making it particularly suitable for quasi-real-time FSPI applications; high-frame-rate real-time imaging still requires further acceleration.