non linear quantization

Hi there!

Can anyone help or give reference about this problem: 

what quantification scheme will be used and how will it be implemented
when i try to render an image in a cellphone screen considering a certain
correction intensity of a square function f(x)=255*sqrt(x/255) and x
ranging from 0 to 255 which represents image intensity? 

i really do appreciate any input.

thanks much,
mousecatz