Is there a known correlation between human voice (360Hz to 5kHz) and the frequencies above/below that? Hello SignalProcessing!

Given the important frequencies of a human voice (360Hz to 5kHz) to communicate and the frequencies above and below that make the voice sound way better.

Imagine we are recording a phone call... the provider normally transmitts only the frequencies needed for moderate communication. I am interested in reconstructing the information for the lost frequencies above and below by training deep neuronal nets.
To improve the training progress it would be helpful to figure out if there is sort of a correlation.

Any reference about that topic would be great!
Thank you.
There is a correlation and it can be learned with machine learning methods. A simple google search can give you many papers, recent research

Waveform Modeling and Generation Using Hierarchical Recurrent Neural Networks for Speech Bandwidth Extension
Zhen-Hua Ling, Yang Ai, Yu Gu, Li-Rong Dai

older paper:

Techniques for the Regeneration of Wideband Speech from Narrowband Speech
Jason A. Fuemmeler, Russell C. Hardie, William R. Gardner