[Schiphol]

> perhaps there is, or should be defined, a signal/noise Kolmogorov Complexity measure

This is studied in so-called algorithmic rate-distortion theory:

Rooij, S. de, & Vitanyi, P. (2012). Approximating Rate-Distortion Graphs of Individual Data: Experiments in Lossy Compression and Denoising. IEEE Transactions on Computers, 61(3), 395–407. https://doi.org/10.1109/TC.2011.25

Vereshchagin, N., & Vitányi, P. (2006). On Algorithmic Rate-Distortion Function. Information Theory, 2006 IEEE International Symposium On, 798–802.