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A convex single image dehazing model via sparse dark channel prior

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  • Wang, Yugang
  • Huang, Ting-Zhu
  • Zhao, Xi-Le
  • Deng, Liang-Jian
  • Ji, Teng-Yu

Abstract

In this paper, we present a convex model for single image dehazing via a sparse dark channel prior. Our work is based on an observation that the number of bright pixels is very small in the dark channel of a haze-free image, but significantly increases in that of a hazy image due to the existence of bright atmosphere light. Since the dehazing problem is inherently ambiguous, we first reformulate the degradation model of hazy images into an equivalent form where the transmission and the image variable are decoupled. With the above formulation and observation, we propose the convex model to recover the haze-free image whose dark channel is assumed to be sparse. The proposed objective function consists of four terms: a data-fitting term, an l1 regularization term for the dark channel of the haze-free image, and two total variation regularization terms for both the haze-free image and the transmission map. We develop an efficient alternating direction method of multipliers (ADMM) to tackle the proposed convex model. Extensive experiments on real hazy images illustrate that our method outperforms the state-of-the-art methods.

Suggested Citation

  • Wang, Yugang & Huang, Ting-Zhu & Zhao, Xi-Le & Deng, Liang-Jian & Ji, Teng-Yu, 2020. "A convex single image dehazing model via sparse dark channel prior," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    • Handle: RePEc:eee:apmaco:v:375:y:2020:i:c:s0096300320300540
    DOI: 10.1016/j.amc.2020.125085
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    References listed on IDEAS

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    1. Patrick L. Combettes & Jean-Christophe Pesquet, 2011. "Proximal Splitting Methods in Signal Processing," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 185-212, Springer.
    2. Yang, Jing-Hua & Zhao, Xi-Le & Ji, Teng-Yu & Ma, Tian-Hui & Huang, Ting-Zhu, 2020. "Low-rank tensor train for tensor robust principal component analysis," Applied Mathematics and Computation, Elsevier, vol. 367(C).
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