AI 中文总结
针对二值化傅里叶单像素成像中空间抖动引入量化误差的问题，提出指数多灰度级计算加权抖动方法，大幅降低傅里叶系数误差，提升成像质量至接近理论分辨率极限。
AI 中文摘要
二值化傅里叶单像素成像（FSI）通过应用Floyd-Steinberg空间抖动对灰度傅里叶图案进行二值化，充分利用了数字微镜器件的高调制速度。然而，空间抖动的使用会引入大量量化误差，导致成像质量下降。本文提出一种基于指数多灰度级计算加权抖动的灰度傅里叶图案二值化方法，旨在减少量化误差，进而提升二值化FSI的成像质量。该方法将傅里叶图案量化为2^R个值{0, 1/(R-1), 2/(R-1), ..., 1}，随后将其分解为二值化图案。仿真与实验结果均表明，该方法显著降低了傅里叶系数采集过程中的量化误差，提升了成像质量。傅里叶系数的平均绝对百分比误差从194%降至28%，重构图像（256×256像素）的结构相似性从0.430提升至0.971，较传统方法提升了126%。该方法的横向分辨率几乎达到了瑞利判据计算得出的理论横向分辨率极限。
英文摘要
Binarized Fourier single-pixel imaging (FSI) takes full advantage of the high modulation speed of digital micromirror devices by applying Floyd-Steinberg spatial dithering to binarize grayscale Fourier patterns. However, the use of the spatial dithering introduces substantial quantization errors, leading to decreasing imaging quality. Here, we propose a binarization method for grayscale Fourier patterns based on exponential multi-graylevel computational-weighted dithering, aimed at reducing quantization errors and then enhancing the imaging quality of binarized FSI. The proposed method quantizes Fourier patterns into $2^{R}$ values $\{0, 1/(R-1), 2/(R-1)... 1\}$ and then decomposes them into binarized patterns. Both simulation and experimental results demonstrate that the method significantly reduces quantization errors in Fourier coefficients acquisition and improves imaging quality. The mean absolute percentage error of Fourier coefficients decreases from $194\%$ to $28\%$ and the structural similarity of reconstructed images ($256\times256$ pixels) improves from 0.430 to 0.971, a $126\%$ enhancement compared to the conventional method. Lateral resolution of this proposed method almost approaches the theoretical lateral resolution limit calculated by Rayleigh Criterion.
