I'm assuming you mean applying a Gaussian blur. Pillow (a Python Image Library fork) supports a lot of image processing methods, including Gaussian blur. The ImageFilter module in particular implements this.
As for how to measure the level of noise--that's a somewhat complicated question. The concepts of radius and variance are mostly related (this post discusses it to some degree). In practicality, for picking the right parameter here for image processing, theory is all well and good but I've found guess and try to be the best way here.
dB is generally related to Gaussian filters (at least on the topic of "Gaussian" things that can act on input signals), as in digital signal processing (DSP). Gaussian blur/filter are similar concepts as convolutions on input signals, but discussed in different domains. When talking about signals in DSP, it's a bit more natural to talk about dB for the filter response... as well as just comparing signals generally. I'm assuming this is not what you're talking about.