Overcoming the Rayleigh limit in extremely low SNR

Overcoming the diffraction limit and addressing low Signal-to-Noise Ratio (SNR) scenarios have posed significant challenges to optical imaging systems in applications such as medical diagnosis, remote sensing, and astronomical observations. In this study, we introduce a novel Stochastic Sub-Rayleigh Imaging (SSRI) algorithm capable of localizing point sources and estimating their positions, brightness, and number in low SNR conditions and within the diffraction limit. The SSRI algorithm utilizes conventional imaging devices, facilitating practical and adaptable solutions for real-world applications. Through extensive experimentation, we demonstrate that our proposed method outperforms established algorithms, such as Richardson-Lucy deconvolution and CLEAN, in various challenging scenarios, including extremely low SNR conditions and large relative brightness ratios. We achieved between 40% and 80% success rate in estimating the number of point sources in experimental images with SNR less than 1.2 and sub-Rayleigh separations, with mean position errors less than 2.5 pixels. In the same conditions, the Richardson-Lucy and CLEAN algorithms correctly estimated the number of sources between 0% and 10% of the time, with mean position errors greater than 5 pixels. Notably, SSRI consistently performs well even in the sub-Rayleigh region, offering a benchmark for assessing future quantum superresolution techniques. In conclusion, the SSRI algorithm presents a significant advance in overcoming diffraction limitations in optical imaging systems, particularly under low SNR conditions, with potential widespread impact across multiple fields like biomedical microscopy and astronomical imaging.