AI 中文总结
针对傅里叶单像素成像，提出几何优化复域误差扩散编码方法，用K个加权二进制图案表示复值傅里叶基图案并在复域扩散残余误差，建立几何解释并开发优化策略，经模拟和实验验证，其重建质量优于传统相移抖动。
AI 中文摘要
本文提出了一种用于傅里叶单像素成像的几何优化复域误差扩散编码方法。该方法不是独立地对多个灰度相移图案进行二值化，而是使用K（K >= 3）个加权二进制图案直接表示每个复值傅里叶基图案，同时在复域中扩散残余误差。进一步建立了几何解释，表明编码过程可视为用复平面中的正多边形逼近傅里叶基单位圆。基于此几何解释，针对K = 3、K = 4和K = 7开发了实际优化策略。数值模拟和实物实验均表明，与传统相移抖动相比，重建质量始终更优。
英文摘要
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.
Comments6 pages, 5 figures
