The demo shows that the synchrosqueezed filterbank representation can be directly used to reconstruct the original signal. Since we do not work with a filterbank which forms a tight frame (its filterbankresponse is not constant) the direct reconstruction (mere summing all the channels) does not work well. We can fix that by filtering (equalizing) the result by the inverse of the overall analysis filterbank frequency response.
N. Holighaus, Z. Průša, and P. L. Søndergaard. Reassignment and synchrosqueezing for general time-frequency filter banks, subsampling and processing. Signal Processing, 125:1--8, 2016. [ DOI | http ]