High-fidelity and ultra low-sampling-rate single-pixel imaging with physically enhanced Laguerre-Gaussian encoding

Single-pixel imaging (SPI) has offered an unprecedented technique for capturing a targeted scenes without requiring raster scanning or muti-pixel detector arrays. Despite its advantages, achieving both high spatial fidelity and ultra-low sampling ratio, particularly below 5%, without additional post-processing algorithms in the existing SPI architectures remains a significant challenge due to that a reconstruction needs a large amount of measurements. To circumvent these challenges, here we demonstrate a novel Laguerre-Gaussian single-pixel imaging (LGSI) framework achieving ultra-low sampling ratio of 3% and super-high spatial imaging fidelity with average structural Similarity (SSIM) of 0.770 and average peak signal-to-noise ratio (PSNR) of 19.140 dB. The fundamental methodology relies on the enhancement of the encoded patterns by discrete orthogonal physical Laguerre-Gaussian (LG) moments in which the measured signals have a higher compression sampling as the dimensionality of the coding LG moments increases. Leveraging this orthogonal mechanism, LGSI demonstrates superior imaging fidelity and computational efficiency, surpassing the capabilities of non-orthogonal moments. Comparative analyses of the power spectra from reconstructed images highlight the enhanced efficacy of LGSI over Hadamard SPI (HSI) and Fourier SPI (FSI). Our results suggest the possibility of encoding multi-dimensional structured light fields as a promising pathway for realizing low sampling ratio, universal, and physical-endow SPI.