how to remove Fog noise without losing fine details

i have done fog removal on an image. i got a noisy image but have fine details like face specialisation. After applying filter, all fine details are blurred. i want to remove entire fog pixels and also need to retain fine details or sharpnesss of image.i tried many additions, filters, and histmatch approaches to solve it, but dont get a satisfactory result. i also tried algorithms like dcp but still i am unable to remove fog efficiently.So please suggest any methods to remove fog efficiently without losing fine details . Please tell can i do anything more on these images or any step to identify noise pixels and remove it. i attached two figs here