spectrogram - Modified STFT resynthesis

This post is basically a follow-up to my recent question, which I asked here How to deal with phase incoherence issues after manipulating a signal in the frequency domain?

In short, I'm modifying the STFT and want to resynthesize a waveform that most closely resembles the modified STFT.

After some research, I found out that the standard way to do this is to implement the Griffin Lim algorithm (or one of its variants). The original paper can be found here https://pdfs.semanticscholar.org/14bc/876fae55faf5669beb01667a4f3bd324a4f1.pdf.

While the algorithm doesn't seem too complicated, I don't think I understand it fully and consequently can't implement it.

I'd appreciate it if someone can have a look at the article and try to explain equation #6 (which is what I need). Some pseudocode/example would be great.

Thank you