Can I convert spectrograms generated with librosa back to audio?

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Yes, it is possible to recover most of the signal and estimate the phase with e.g. Griffin-Lim Algorithm (GLA). Its “fast” implementation for Python can be found in librosa. Here’s how you can use it:

import numpy as np
import librosa

y, sr = librosa.load(librosa.util.example_audio_file(), duration=10)
S = np.abs(librosa.stft(y))
y_inv = librosa.griffinlim(S)

And that’s how the original and reconstruction look like:

reconstruction

The algorithm by default randomly initialises the phases and then iterates forward and inverse STFT operations to estimate the phases.

Looking at your code, to reconstruct the signal, you’d just need to do:

import numpy as np

X_inv = librosa.griffinlim(np.abs(X))

It’s just an example of course. As pointed out by @PaulR, in your case you’d need to load the data from jpeg (which is lossy!) and then apply inverse transform to amplitude_to_db first.

The algorithm, especially the phase estimation, can be further improved thanks to advances in artificial neural networks. Here is one paper that discusses some enhancements.

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