There are single ended NR systems, mainly involving downwards expansion and/or dynamic filtering, but most good systems are double ended with complementary encode / decode systems.
The simplest is the pre-emphasis / de-emphasis idea, with fixed eq boosting hf on the way in, with the opposite eq on the way out to provide overall flat response, but pushing the medium noise down in the more audible hf region at the same time.
Then there are the compander systems, reducing the dynamic range of the input signal into the medium, and then expanding it back again on the output, pushing all the system noise down along the way. Of course, such systems have tracking issues which may result in audible side effects. The various dbx systems worked along these lines.
Dolbys approach to improve this problem was to split the audio into separate bands and comp and each independently, relying on noise masking within each band to hide the artefacts. Dolby SR took the idea much further than Dolby A, and was very good, but came out as digital took off, so didn't really gain the familiarity it deserved. Dolby b, c and s were simplified domestic systems with less nr efficiency and more artefacts.
dolbys main competitor in Europe was telecom with it's c4 system, worth checking out. Dolbys website has a lot of very good White papers on the technology involved.
It is also worth noting that a lot of the ideas behind effective noise reduction translate to digital data reduction, in the various frequency and temporal noise masking processes involved in hiding the processing artefacts.
Studio Sound magazine had a lot of good articles about this stuff back in the late 1970s and 80s if your library has them.
Technical Editor, Sound On Sound