  The Rayleigh limit and low Signal-to-Noise Ratio (SNR) scenarios pose
significant limitations to optical imaging systems used in remote sensing,
infrared thermal imaging, and space domain awareness. In this study, we
introduce a Stochastic Sub-Rayleigh Imaging (SSRI) algorithm to localize point
objects and estimate their positions, brightnesses, and number in low SNR
conditions, even below the Rayleigh limit. Our algorithm adopts a maximum
likelihood approach and exploits the Poisson distribution of incoming photons
to overcome the Rayleigh limit in low SNR conditions. In our experimental
validation, which closely mirrors practical scenarios, we focus on conditions
with closely spaced sources within the sub-Rayleigh limit (0.49-1.00R) and weak
signals (SNR less than 1.2). We use the Jaccard index and Jaccard efficiency as
a figure of merit to quantify imaging performance in the sub-Rayleigh region.
Our approach consistently outperforms established algorithms such as
Richardson-Lucy and CLEAN by 4X in the low SNR, sub-Rayleigh regime. Our SSRI
algorithm allows existing telescope-based optical/infrared imaging systems to
overcome the extreme limit of sub-Rayleigh, low SNR source distributions,
potentially impacting a wide range of fields, including passive thermal
imaging, remote sensing, and space domain awareness.
