White noise is random, so it's incompressible by definition. By JPG or by any other method no matter how clever.

I have a very peculiar coin. With 1% probability it turns up heads and with 99% probability it turns up tails.

A string of flips is random, but it's very compressible.

In any case, my point was that reality ain't uniformly random. And not only that: pretty much anything you can point your camera at shares enough similarity in their distribution that we pretty much have universal compression algorithms for real world data.