Does an equivalent transformation of a signal to a spectrogram image exist in which the phase information is part of the resulting image? I'm working on a research project where we would like to apply convolutional neural networks to an image representation of a signal. However, it seems that if I would use a spectrogram, I would end up loosing the phase information. As a result, my question is:

Does an equivalent transformation of a signal to a spectrogram image exist in which the phase information is part of the resulting image?

Thanks a lot and have a great day, Maxime

From https://en.wikipedia.org/wiki/Spectrogram:


  Limitations and resynthesis
  
  From the formula above, it appears that a spectrogram contains no
  information about the exact, or even approximate, phase of the signal
  that it represents. For this reason, it is not possible to reverse the
  process and generate a copy of the original signal from a spectrogram.
If you create a volumetric (unflattened 3D) image, you can use 2 layers in the 3rd dimension to represent magnitude and phase, or real and imaginary components of a complex spectrogram output.

In a 2D color spectrogram, you could try using an orthogonal color mapping, for instance, in RGB space, red + green for magnitude and blue (or delta blue) for phase, or similar for real and imaginary components, or use YUV or HSL color spaces, etc.