Scene recovery from real-world images degraded by scattering effects, such as haze, sandstorm, underwater, and remote sensing conditions, remains a fundamental yet challenging problem in computer vision. Existing methods either rely on a single prior, which is inherently insufficient to characterize diverse scattering degradations, or employ deep networks trained on synthetic data, which often suffer from limited generalization to real-world scenarios. In this paper, we propose Spatial and Frequency Priors (SFP) for real-world scene recovery under scattering-induced degradations. In the spatial domain, we observe that the inverse of a scattering-degraded image reveals a projection along its spectral direction that correlates with the underlying scene transmission. Based on this observation, a spatial prior is formulated to estimate the transmission map, enabling effective recovery of scene radiance under scattering effects. In the frequency domain, we design an adaptive frequency enhancement strategy guided by two novel priors. The first prior assumes that the mean intensity of the direct current (DC) components across channels in degraded images approximates that of the corresponding clear images. The second prior is based on the observation that, in clear images, low radial frequencies within a narrow band contribute only a small proportion of the overall spectrum. These priors enable targeted compensation for scattering-induced attenuation across different frequency bands. Finally, a weighted fusion of the spatial and frequency domain results is performed to obtain the final recovered image. Extensive experiments on diverse real-world scattering-degraded scenarios verify that our SFP achieves superior performance and strong generalization capability compared to state-of-the-art methods.