Aiming at the problem of scene degradation in haze and sandy weather, a degraded scene restoration algorithm based on convex optimization of Gaussian model and double constraints of light curtains is proposed. First, according to the correlation between depth of field and scene brightness and saturation, Gaussian model and convex optimization are used to estimate depth of field. Second, the relationship between atmospheric light curtain and scene is deeply analyzed, and the atmospheric light curtain of degraded scene is obtained by combining minimum channel smoothing and depth-of-field attenuation constraints. Then, the atmospheric light value is obtained through the improvement of the bright channel a priori and the local atmospheric light. Finally, the degraded scene is restored based on the restoration model, and the color of the sand and dust scene is corrected to realize the scene restoration. The experimental results show that the restored scene of the proposed algorithm has suitable brightness, natural color and rich detail information. It can also obtain an ideal score in the quantitative index, which can effectively solve the problems of color cast and detail loss in degraded scenes.