Mitigating Out-of-Focus Noises in Single-Molecule Localization via the Orientation-aware Deep Network

Abstract Single-molecule localization microscopy (SMLM) typically degrades in thick perinuclear regions due to structured noise from out-of-focus fluorescence, which obscures signals and biases localization. Here, we present ORIENCODE, a deep-learning framework that leverages an Euler’s elastica energy model to robustly distinguish in-focus emitters from diffuse interference based on morphological signatures. By enforcing joint constraints on boundary length and curvature, the network integrates geometric perception with adversarial training and a Cramér–Rao lower bound-anchored loss to minimize uncertainty. Quantitative experiments demonstrate that ORIENCODE achieves an axial localization precision of approximately 18 nm under challenging out-of-focus noise conditions, representing an improvement of more than 10 nm compared to standard Gaussian fitting methods. We further show that the proposed method enables high‑fidelity structural reconstruction of mitochondria and microtubules within thick perinuclear regions, as well as densely labeled actin filaments, effectively overcoming the artifacts that limit conventional methods.