Is it possible to clean up an audio recording of a lecture from a smartphone (i.e. remove the background noise) using some type of AI system?
Yes, it is possible. Usually, the noise reduction is done using regular signal processing methods, such as spectral subtraction due to demand for low latency. But, of course, modern methods of deep learning are applicable to this problem. For example, the variational autoencoder is the first that comes to my mind, you can check this project. Another example you can look at is this project, which is based on WaveNet.