Re-scaling back a function

Question

I am implementing an algorithm known as Enhanced Lee's Algorithm in python, which is used in de-noising and enhancing an image. Algo is as given below:

1. Image matrix F is transformed to a grey tone function: F(x,y) = L-R(x,y) , where L is 256 and R is intensity value of image at coordinate x,y

2. Now grey tone function is transformed to normalized negative grey tone function such as , fbar=1-f/L

3. Algo is implemented:

log(f'bar(x,y))= betalog[kbar(x,y)] + psi[log(fbar(x,y)-log(kbar(x,y)] , kbar is local mean value, beta and psi are parameters.

Now , as per paper we will get enhanced image , once we **convert f' back to original scale, to obtain F' enhanced image **

Here, I am facing issue, how should I scale f' back to original scale? Please help me get it.

Thanks in advance. Here is the image of algo:

Image of the algorithm from paper