I agree with your point, but you're arguing that noise can be redundant data. I am arguing that redundant data is not necessarily noise.
In other words, a signal can never be filtered losslessly. You can slap a low pass filter in front of the signal and call it a day, but there's loss, and if lossless is a hard requirement then there's absolutely nothing you can do but work on compressing redundant data through e.g. patterns, interpolation, what have you (I don't know much about compression algos).
A perfectly noise free signal is arguably easier to compress actually as the signal is more predictable.