ing at problem that the single image clearness algorithm cannot guarantee the effect of noise and fog reduction, a new algorithm for foggy and noisy single image clearness using the lazy random walk model is proposed. Firstly, physical meaning of existing atmospheric scattering model is analyzed and improved to be made more consistent with the specialist of the actual foggy images. Lazy random walk model is used to estimate the attenuation term of improved haze degeneration model. Secondly, geometric constraint and color-line prior are used to obtain accurate atmospheric light of the degeneration model. Fog-free images with little noise are recovered at last. Experimental results show that the proposed algorithm can obtain the best defogging effect and restrain the noise, and it has strong robustness.