Algorithm for Fog-degraded Image Enhancement Based on Adaptive Fractional-order PDE

In this study, an image enhancement model based on an inverse diffusion equation with a Riesz fractional derivative is developed. The optimal orders of fractional derivatives for the images are obtained through experiments, and six quantities associated with the brightness and texture of each haze image—mean, variance, skewness, kurtosis, two-norm, and contrast—are calculated. By regression analysis, the linear relationship between the optimal order of the fractional derivative and these statistical quantities is acquired. Finally, the empirical formula for the order of the fractional derivative for the differential equation model is obtained. Experimental results show that the adaptive order of the fractional differential obtained using our approach is close to the optimal order obtained using artificial experiments and that the enhancement effect is optimal. Compared with other image enhancement algorithms, our algorithm can better improve the brightness and contrast of images and provide a better visual effect while defogging. Two objective evaluation indexes— information entropy and average gradient—also indicate the effectiveness of our method.