Single image dehazing is an ill-posed problem of the image degradation model. Many researches focused on the problem in estimating the atmospheric light intensity and the medium transmission. A simple but effective interval estimation method was proposed to quickly remove haze from a single input image in a new perspective. Firstly, scope of interval estimation was reduced by discussing on atmospheric light intensity and medium transmission. Secondly, the fast joint bilateral filtering and median filtering were adopted to optimize the edge regions of medium transmission. And by the absolute value of the difference of atmospheric light and dark channel, the bright areas can be judged and amended. Finally, the tone mapping was used to refine the performance of the restored image. Experimental results demonstrate that the proposed method can clearly improve the computational speed and obtain a better restoration effect compared to some state-of-the-art methods.