How to reconstruct a sound from magnitude spectrogram? I have an audio magnitude spectrogram but I don't have the phase, try to randomize the phases of each container and then make a reverse fourier, but only pure noise is heard

How can I reconstruct the phase information so that the audio is heard somewhat decent.

Anyone know an algorithm that does this?
In general the whole complex Fourier transform is needed to reconstruct the time domain signal. 

However, it's possible to reconstruct a real signal it from its Fourier transform magnitude alone (or phase alone) by using some iterative techniques, or very large matrix solutions.

Have a look at the papers by Monson Hayes...