Abstract: The contrast and visibility of outdoor images taken in hazy weather are seriously affected. At
present, the image dehazing methods usually consider that the dehazing performance highly depend
ends on the accurate transmission image. The second order Hessian regular term has the ability to
preserve fine structure and suppress step artifacts, which is helpful to improve the image contrast and
visibility. Therefore, in this paper, the dark channel prior method is first used to obtain atmospheric
optical value and the initial transmission image, and then a second order variational model is proposed
to refine the initial transmission image and dehazing image by combining Hessian regular term. In order
to improve the operational efficiency of the proposed dehazing model, a corresponding alternating
direction multiplier method (ADMM) was designed. By introducing auxiliary variables, the Lagrangian
multiplier was continuously updated and iterated until the energy equation converged. At last, the
simulation experiment was carried out by the foggy image data base (LIVE Image Defogging) to test
the proposed fog removal method. The visual quality and quantitative evaluation of the effect pictures
of mist and fog removal showed that the fog removal images obtained by the fog removal model
proposed in this paper were clear and natural, and the texture details maintained well.

Key words: dark channel prior, transmission image, Hessian regular term, second order variational
model, alter direction method of multipliers