Uncertainty-Aware Airlight-Aligned Dual-Gain Recovery with Exact RGB Feasibility for Training-Free Single-Image Dehazing
The inverse atmospheric-scattering model amplifies transmission, airlight, and sensor-noise errors when a scalar gain $1/t$ is applied in dense haze. We introduce A$^2$CR, a training-free recovery operator that decomposes the airlight-centered RGB residual into components parallel and perpendicular to the airlight vector. Two gains are obtained from analytic quadratic risks containing transmission, airlight, and noise uncertainty. Each gain pair is constrained by the exact convex polygon induced by the six RGB-cube inequalities and gain bounds. An edge-aware joint total-variation problem is solved with a primal-dual algorithm and exact polygon projection. On a controlled DIODE RGB-D evaluation comprising 500 frames and 22,500 reproducible haze recipes, the full variant improves over scalar inversion by $2.951$ dB PSNR (95% bootstrap CI $[2.900,3.001]$), $0.191$ SSIM $[0.187,0.196]$, and $-0.978$ CIEDE2000 $[-1.074,-0.883]$, while eliminating post-recovery RGB violations. Results on four real paired datasets are mixed and were not blind: the method is strongest on Dense-Haze but does not dominate RFEP, DCP, and Haze-Lines elsewhere. We therefore claim an interpretable constrained recovery study, not state-of-the-art dehazing. Code, 64 executable numerical and regression tests, manifests, and statistical artifacts accompany the paper.