Improve image quality by quantization

Question

I know it is possible to convert high level image format like PNG into low level format like GIF as we have all the data and we can decide what to keep and what to spare.. or for example convert 256 colors image into black and white.

The question is what happens in other way. What if I have a black and white picture and i want to convert it to 256 colors. Can it be done? will it be too noisy? or for example if I have a really high quality image with range of 2^20 colors and i'd like to convert it to 2^21 colors... will it be better but my eye won't see the difference?

basically my question is what if i'd like to add more levels instead of reducing. (it also applies to sound if i have mono sound file and i'd like to convert it to wav). levels can indicate colors or whatever... of curse it won't be perfect but can it be done?

Answer 1

you have no gain by doing so, since you do not have more information. Low level example: you have a bit so it can be one or zero: b = [0 1]. Now you store that bit in 2 bit field. It will still have the value 0 or 1, so the rest of the bitfield is simply unused since there is no information to fill it with. The same for your image example: you have 2^20 colors you want to sort them in 2^21 bins. this leaves some of the bins empty. no gain here.

you can use methodes to fill those level, like interpolation but this will not make additional information "appear".