How can you 'perfectly' reconstruct phase for transients in a modified audio absolute spectrogram? I am currently working on the absolute spectrogram of an input audio signal. I am using non-negative matrix factorization to separate out the rhythmic components (bass drum, snare drum and hi-hat) of the file and shift around the activations of these components to get a modified spectrogram. 

Now, I want to reconstruct the phase for this modified spectrogram so that I can take an inverse FFT and recreate the audio signal in time domain. I am currently using the Griffin Lim and the Phase Gradient Heap Integration methods from this phase retrieval toolbox. Unfortunately, this doesn't produce good results. Maybe it's with the arguments I'm using. I'm currently using a window size of 2048 with a hop of 512.

1, 2 - These questions were previously posted where the idea of reconstruction of audio from absolute spectrogram was tackled. This question pertains to how well one can reconstruct the audio signal back in the time domain and what would be the best way to do so when the harmonic content would be the same but the transients would be time-shifted. Also, how would you objectively or subjectively evaluate such a system formally?

Thanks!
Real Time Iterative Spectrum Inversion would be a way to tackle that problem. Have a look at this paper:

IMPROVING RTISI PHASE ESTIMATION WITH ENERGY ORDER AND PHASE
UNWRAPPING