Under the nighttime haze environment, the quality of acquired images will be deteriorated significantly owing to the influences of multiple adverse degradation factors. In this paper, we develop a multi-purpose oriented haze removal framework focusing on nighttime hazy images. First, we construct a nonlinear model based on the classic Retinex theory to formulate multiple adverse degradations of a nighttime hazy image. Then, a novel variational Retinex model is presented to simultaneously estimate a smoothed illumination component and a detail-revealed reflectance component and predict the noise map from a pre-processed nighttime hazy image in a unified manner. Specifically, an

${\ell _{0}}$

norm is imposed on the reflectance to reveal the structural details and we make use of

$\ell _{1}$

norm to constrain the piece-wise smoothness of the illumination and apply

${\ell _{2}}$

norm to enforce the total intensity of the noise map. Afterwards, the haze in the illumination component is removed based on prior-based dehazing method and the contrast of the reflectance component is improved in the gradient domain. Finally, we combine the dehazed illumination and the improved reflectance to generate the haze-free image. Experiments show that our proposed framework performs better than famous nighttime image dehazing methods both in visual effects and objective comparisons. In addition, the proposed framework can also be applicable to other types of degraded images.

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