There were many noise reduction units marketed several decades ago, aimed at rumble, surface noise, pops, clicks, and dynamic range expansion and peak unlimiting. Some, like Bob Carver's Autocorrelator, were very "clever". All worked reasonably well, but none were perfect. Today's vinyl fans prefer to say that all these LP problems either don't exist or can be eliminated by some rather exotic and expensive turntables, pickups, and arms. Whatever...
The only really good way to restore old LPs is to play them back as well as you can, and digitize the signal. Once that is done many techniques can be used that are quite impossible if you try to do the cleanup in real time (while the LP is playing). An example is playing the music backwards. Music has leading edge transients that are similar to clicks and pops, but music has no trailing edge transient...the sound dies away over some time. If you analyse the digital signal forwards and backwards, the clicks and pops, which are transients both ways, can be distinguished from musical transients which only occur with forward playback. I have not actually used this type of LP cleanup software, but the results I have heard far exceed those of the old boxes of electronics.
The only really good way to restore old LPs is to play them back as well as you can, and digitize the signal. Once that is done many techniques can be used that are quite impossible if you try to do the cleanup in real time (while the LP is playing). An example is playing the music backwards. Music has leading edge transients that are similar to clicks and pops, but music has no trailing edge transient...the sound dies away over some time. If you analyse the digital signal forwards and backwards, the clicks and pops, which are transients both ways, can be distinguished from musical transients which only occur with forward playback. I have not actually used this type of LP cleanup software, but the results I have heard far exceed those of the old boxes of electronics.