I would appreciate it if you would give me an answer to my question:
Is it possible to convert the spectrogram image (not the array) to wav (reconstruct the wav audio from the spectrogram in image form)?
Yes this possible. But it will be scaled to 0..255 range as image. Before use it need again normalize something like this for exaple image * (1/255) * 13 -11 and you will get range of mel spectrogram -11..2