Sound finally decomposed into basic components

Sounds pretty neat! I wonder what kind of new instrument/effect plug-ins this will spawn. I haven't read the paper yet, but I'm curious about the 'vibrato' problem that the article mentions. I'm guessing the issue is analyzing a signal in a way that doesn't lose the vibrato when it encodes (ie: to sines, noise, transients), not a limitation of decoding a signal (ie: if it were possible to obtain perfect data)?

This paper is a far better argument for psycho-acoustic components of sound : https://www.nature.com/articles/nature04485/

Transients modeled with wavelets?