Exponential multi-graylevel computational-weighted dithering for high-quality binarized Fourier single-pixel imaging

Abstract

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.