ffmpeg reduce background noise

Question

Audacity has a great noise reduction process that I've found works very well: select a "quiet" sample section of audio, choose Effects>Noise Reduction>Get Noise Profile. Then select whole stream, choose Noise Reduction again, click Ok. I assume it works by finding the power spectral density of the sample and by what means it attenuates that signature from the whole stream, I'm not sure. I assume noise reduction by this means is dependent on how good of a representation the sample is of noise across the entire stream.

I want to automate this with ffmpeg: automatically find a "quiet" section of audio (or ideally, several, and comparing them to compare their likeness), where quiet would be those section with the lowest SNR, and then convoluting this sample with the whole stream. I don't know what convolution filter Audacity uses.

Any ideas how to do this? Would a custom plugin have to be written for ffmpeg to find quiet sections?