Geometry-optimized complex-domain error-diffusion encoding for Fourier single-pixel imaging

This work proposes a geometry-optimized complex-domain error-diffusion encoding framework for Fourier single-pixel imaging. Instead of independently binarizing multiple grayscale phase-shifting patterns, the proposed framework directly represents each complex-valued Fourier basis pattern using K (K≥3) weighted binary patterns while diffusing the residual error in the complex domain. This distinction establishes the proposed framework as a complex-domain counterpart to conventional phase-shifting encoding. A geometric interpretation is further established, revealing that the encoding process can be viewed as approximating the Fourier-basis unit circle by the regular polygon formed by the candidate point set in the complex plane. Based on this geometric interpretation, the encoding performance is further optimized, yielding three representative practical configurations for K=3, K=4, and K=7. The high-temporal-resolution K=3 and K=4 configurations outperform conventional three-step and four-step phase-shifting dithering at matched measurement overhead, while K=7 favors reconstruction quality over temporal resolution.