Parametric Analytical Modulation Transfer Function Model in Turbid Atmosphere with Application to Image Restoration

To address the issues of image blurring and color distortion in hazy conditions, an image restoration method based on a parametric analytical modulation transfer function model is proposed under turbid atmospheric conditions. A source database is established using a numerical radiative transfer method based on discrete ordinate. Through multivariate nonlinear fitting and linear interpolation, the quantitative relationships among critical spatial frequency, turbid atmospheric MTF, and key atmospheric optical parameters—such as optical thickness, single scattering albedo, and asymmetry factor—are examined. A fast and efficient parametric analytical MTF model for turbid atmospheres is developed and applied to restore images affected by fog. The results demonstrate that, within the applicable range of the model, the model’s maximum mean relative error and the root mean square error are 7.16% and 0.0454, respectively. The computational speed is nearly a thousand times faster than that of the numerical radiative transfer method, achieving high accuracy and ease of application. Images restored using this model exhibit enhanced clarity and quality, effectively compensating for the degradation in image quality caused by turbid atmospheres. This approach represents a novel solution to the challenges of image processing in complex atmospheric environments.