A density-aware path-integral and forward-scattering imaging model for single-image dehazing in non-homogeneous fog

Single-image dehazing through non-homogeneous fog is an ill-posed inverse problem at the interface of imaging through scattering media and real-time perception. It raises two coupled difficulties, namely, spatially inconsistent degradation in which thin and dense fog coexist at different depths and the need for a controllable inverse solution under a tight latency budget. Most physics-guided networks estimate transmission implicitly and apply roughly uniform restoration across the scene, without jointly modeling path-integral extinction and forward-scattering diffusion under a single density field. Attention- and transformer-based methods raise the restoration quality but incur an order-of-magnitude increase in the inference cost. We propose UPFS-Dehaze, which couples a density-aware path-integral imaging formulation with a latency-aware unrolled optimization module governed by a spatially weighted Barzilai–Borwein step-size field. Within a fixed-depth three-stage update chain, path-integral extinction and forward-scattering diffusion are jointly modeled through a single estimated haze density field; forward scattering enters as a learned density-modulated scattering field that serves as a tractable surrogate for the underlying kernel integral. The result is region-adaptive restoration at an explicitly bounded inference cost. On the synthetic RESIDE SOTS-outdoor benchmark, the model attains 29.66 dB PSNR and 0.972 SSIM at 0.018 s per image, placing it on the upper-left Pareto frontier of the quality–efficiency trade-off. On two real-fog benchmarks—O-HAZE and the more challenging NH-HAZE (NTIRE 2020)—it attains the highest absolute PSNR among the evaluated zero-shot baselines, with a synthetic-to-real PSNR drop of 9.55 dB on O-HAZE and 10.54 dB on NH-HAZE, against 17.14 dB and 18.10 dB for the highest-PSNR synthetic baseline. Together, these results indicate that unifying extinction and forward scattering under a single density field and solving the inverse problem with a latency-bounded unrolled optimizer supports image restoration through non-homogeneous scattering media without sacrificing real-time inference.