Spectrogram FFT as Matrix (back and forth)

Dear all,
I am trying to convert a sound into a 2D spectrogram (via FFT) where the X-axis is the FFT per frame and the Y-axis is the time.
Basically I want to create a matrix that captures the sound of one second.

In the next step I want to also play back from that matrix - without noticable/strong quality loss.
So the temporal resolution should be good.

So far I didn't manage to solve it.
I looked at fft~ and jit.poke and also jit.catch - but didn't get it to work yet.

This is what I have so far:

Can anybody point me to a solution for this?
Best, Frank