What are some alternatives to Spectrogram charts? Spectrogram renders of audio are limited in their representation of audio. For example, one could not use a Spectrogram to re-render the original audio.

What are some alternatives to Spectrogram charts for rendering representations of audio? 

Preferably this would be methods which are more accurate (in every possible way/in every possible audio dimension) for representing audio in graphical format (an image)?

A good measure of accuracy would be for example;


Could the image be used to (at least to some extent) re-create the audio file?
Could the image be used to match the similarity between two songs in some or all dimensions?


And, are there any scripts/tools/software's that can be used for converting audio into an image format?
The ltfatpy 1.0.16 package 


  is a partial Python port of the Large Time/Frequency Analysis Toolbox
  (LTFAT), a MATLAB®/Octave toolbox for working with time-frequency
  analysis and synthesis.


Among linear and quadratic time-frequency methods, there is a large number of options for sharper analysis tools converting a 1D signal into 2D data. You can even get more information by decomposing onto 3D or 4D spaces (coming back on that later). Quadratic (or higher-order) representations are usually more difficult to invert than linear ones. 

And here is a documentation for ltfatpy.