Wavelet decomposition of images

I'm wondering if an image such as http://en.wikipedia.org/wiki/File:Jpeg2000_2-level_wavelet_transform-lichtenstein.png is just a representation of a wavelet decomposition, or if you could actually recover the decomposed image.

The decomposition code works with doubles, so while I can decompose an image properly (each colour channel separately), the resultant values are doubles and some of them are outside the 0-255 range. I'm not sure if it's possible to represent the result as an image and then reverse the decomposition, since I'd have to transform the values to bytes and I'd lose a shitload of precision.

>>4
I'm trying to implement a denoising filter and I think that I can simply work entirely with doubles; I'm just wondering if images such as the one linked in the OP are only representations of the wavelet decomposition or if they're actually usable.