Geometry-Optimized Complex-Domain error-diffusion encoding for Fourier Single-Pixel Imaging

Abstract

This work proposes a geometry-optimized complex-domain error-diffusion encoding method for Fourier single-pixel imaging. Instead of independently binarizing multiple grayscale phase-shifting patterns, the proposed method directly represents each complex-valued Fourier basis pattern using K (K >= 3) weighted binary patterns while diffusing the residual error in the complex domain. A geometric interpretation is further established, revealing that the encoding process can be viewed as approximating the Fourier-basis unit circle by a regular polygon in the complex plane. Based on this geometric interpretation, practical optimization strategies are developed for K = 3, K = 4, and K = 7. Both numerical simulations and real-object experiments demonstrate consistently superior reconstruction quality compared with conventional phase-shifting dithering.