Undersampling Fourier single-pixel imaging based on array spatial light field modulation

Fourier single-pixel imaging (FSPI) can operate with partial Fourier measurements, although reconstruction deteriorates at very low sampling rates. We combine tiled array-Fourier modulation with a dual residual network incorporating Global Attention Mechanism blocks (DuRN-GU). The tiled patterns encode several spatial subregions in each projection. Detector readings are arranged as a two-dimensional map and reconstructed directly, without first forming an inverse-Fourier image. A linear analysis of the sensing operator shows that increasing the array partitioning factor reduces the number of distinct patterns but enlarges the null space and mixes information from more subregions; we therefore use a 2 × 2 array for the main experiments and a 4 × 4 array to study this trade-off. At sampling rates as low as 0.195%, experiments on MNIST, fly32, and Fashion-MNIST show a clear improvement over conventional IFFT-FSPI and competitive performance relative to the learning-based methods considered here. The GAM ablation yields consistent gains on MNIST, and the 4 × 4 results exhibit the predicted increase in inter-subregion mixing. A representative experiment on a 256 × 256 -pixel target and optical measurements of handwritten digits and a grayscale non-digit target indicate that direct measurement-to-image reconstruction remains effective at higher resolution and with experimental nonidealities.