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An Effective Algorithm for Single Image Fog Removal


Poor visibility due to the effects of light absorption and scattering is challenging for processing images captured in foggy weather conditions. This paper proposes an effective algorithm for single image fog removal based on degradation model and group-based sparse representation (GSR). The proposed degradation model is constructed based on a classical physical model, i.e., dichromatic atmospheric scattering model. Then, the new degradation model is integrated into the group-based sparse representation framework. Finally, the single image defogging problem is regarded as an image restoration problem, which can be well optimized by GSR. The method is compared with several well-known algorithms from the literature using qualitative and quantitative evaluations, and results indicate considerable improvement over existing algorithms.

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  1. 1.

    Xie CH, Qiao WW, Liu Z (2016) Single image dehazing using kernel regression model and dark channel prior. SIViP 11:1–8

    Google Scholar 

  2. 2.

    Tripathi AK, Mukhopadhyay S (2014) Efficient fog removal from video. SIViP 8(8):1431–1439

    Article  Google Scholar 

  3. 3.

    Kim TK, Paik JK, Kang BS (1998) Contrast enhancement system using spatially adaptive histogram equalization with temporal filtering. IEEE Trans Consum Electron 44(1):82–87

    Article  Google Scholar 

  4. 4.

    Al-Sammaraie MF (2015) Contrast enhancement of roads images with foggy scenes based on histogram equalization. In: Proc. the 10th int. conf. comput. sci. educ., pp 95–101

  5. 5.

    Zhou J, Zhou F (2013) Single image dehazing motivated by retinex theory. In: Proc. the 2nd int. symposium. instrum. meas. sens. net. automat, pp 243–247

  6. 6.

    Mei X, Yang J, Zhang Y, Li W, Zhang J (2016) Video image dehazing algorithm based on multi-scale retinex with color restoration. In: Proc. the int. conf.. smart grid elec. automat., pp 195–200

  7. 7.

    Grewe LL, Brooks RR (1998) Atmospheric attenuation reduction through multisensor fusion. Proc SPIE 3376:102–109

    Article  Google Scholar 

  8. 8.

    Tarel JP, Hautière N (2009) Fast visibility restoration from a single color or gray level image. In: Proc. IEEE int. conf. comput. vision, pp 2201–2208

  9. 9.

    Tarel JP, Hautière N, Cord A, Gruyer D (2010) Improved visibility of road scene images under heterogeneous fog. In Proc. IEEE intell. veh. symposium, 23(3):478–485

  10. 10.

    Oakley JP, Satherley BL (1998) Improving image quality in poor visibility conditions using a physical model for contrast degradation. IEEE Trans Image Process 7(2), pp 167–179

    Article  Google Scholar 

  11. 11.

    Narasimhan SG, Nayar SK (2003) Interactive (de)weathering of an image using physical models. In: Proc. ICCV workshop color photometric methods in comput. vis., pp 1–8

  12. 12.

    Wang X, Tang Z (2008) Automatic image de-weathering using physical model and maximum entropy. In: Proc. IEEE Conf. Cybernetics Intell. Syst., pp 996–1001

    Google Scholar 

  13. 13.

    He K, Sun J, Tang X (2011) Single image haze removal using dark channel prior. IEEE Trans Pattern Anal Mach Intell 33(12):2341–2353

    Article  Google Scholar 

  14. 14.

    Lai Y, Chen Y, Chiou C, Hsu C (2015) Single-image dehazing via optimal transmission map under scene priors. IEEE Trans Circ Syst Video Technol 25(1):1–14

    Article  Google Scholar 

  15. 15.

    Elad M, Aharon M (2006) Image denosing via sparse and redundant representations over learned dictionaries. IEEE Trans Image Process 15(12):3736–3745

    MathSciNet  Article  Google Scholar 

  16. 16.

    Dong W, Zhang L, Shi G, Wu X (2011) Image deblurring and superresolution by adaptive sparse domain selection and adaptive regularization. IEEE Trans Image Process 20(7):1838–1857

    MathSciNet  Article  Google Scholar 

  17. 17.

    Yang J, Wright J, Huang T, Ma Y (2010) Image super-resolution via sparse representation. IEEE Trans Image Process 19(11):2861–2873

    MathSciNet  Article  Google Scholar 

  18. 18.

    Zhang J, Zhao D, Gao W (2014) Group-based sparse representation for image restoration. IEEE Trans Image Process 23(8):3336–3351

    MathSciNet  Article  Google Scholar 

  19. 19.

    Banham MR, Katsaggelos AK (1997) Digital image restoration. IEEE Signal Process Mag 14:24–41

    Article  Google Scholar 

  20. 20.

    Nayar SK, Narasimhan SG (1999) Vision in bad weather. In: Proc. IEEE int. conf. comput. vis., pp 820–827

  21. 21.

    Li X (2011) Image recovery from hybrid sparse representation: a deterministic annealing approach. IEEE J Sel Top Sign Process 5(5):953–962

    Article  Google Scholar 

  22. 22.

    Mairal J, Bach F, Ponce J, Sapiro G, Zisserman A (2009) Non-localsparse models for image restoration. In: Proc. IEEE 12th int. conf.comput. vis., pp 2272–2279

  23. 23.

    Dong W, Zhang L, Shi G, Li X (2013) Nonlocally centralized sparserepresentation for image restoration. IEEE Trans Image Process 22(4):1620–1630

    MathSciNet  Article  Google Scholar 

  24. 24.

    Aharon M, Elad M, Bruckstein A (2006) K-SVD: an algorithm fordesigning overcomplete dictionaries for sparse representation. IEEE Trans Signal Process 54(11):4311–4322

    Article  Google Scholar 

  25. 25.

    Schechner YY, Averbuch Y (2007) Regularized image recovery in scattering media. IEEE Trans Pattern Anal Mach Intell 29(9):1655–1660

    Article  Google Scholar 

  26. 26.

    Zhang L, Zhang L, Mou X, Zhang D (2011) FSIM: a feature similarity index for image quality assessment. IEEE Trans Image Process 20(8):2378–2386

    MathSciNet  Article  Google Scholar 

  27. 27.

    Wang J, He N, Zhang L, Lu K (2015) Single image dehazing with a physical model and dark channel prior. Neurocomput. 149:718–728

    Article  Google Scholar 

  28. 28.

    Tripathi AK, Mukhopadhyay S (2012) Single image fog removal using anisotropic diffusion. IET Image Process 6(7):966–975

    MathSciNet  Article  Google Scholar 

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This work was supported in part by the Fundamental Research Funds for the Central Universities (Grant No. 2019B15314, 30918014107), in part by the National Natural Science Foundation of China (Grant No. 61603124), in part by the Jiangsu Government Study Scholarship, in part by the Six Talents Peak Project of Jiangsu Province (Grant No. XYDXX-007), and in part by the 333 High-Level Talent Training Program of Jiangsu Province.

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Correspondence to Xin Wang.

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Wang, X., Zhang, X., Zhu, H. et al. An Effective Algorithm for Single Image Fog Removal. Mobile Netw Appl 26, 1250–1258 (2021).

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  • Image restoration
  • Fog removal
  • Degradation model
  • Group sparse representation