Power Spectral Density Reconstruction
A few observations

Your pictures looks odd. &quot;Wave 1&quot; doesn't look like an original audio file but something that has already been encoded/decoded and aggressively lowpass filtered in the process. Your reconstructed audio (Wave 2) actually as MORE high frequency energy, which I suspect is simply just quantization noise from the other bands. The expected spectrum of music is roughly pink (3dB/octave) up to about 10 kHz and then a steeper decline (maybe 10dB octave) to 20 kHz and above. There shouldn't be a step function in the spectrum.
The standard method of recovering for lost high frequency spectrum is Spectral Replication. That's been already implemented in some of the more modern codec standards (e.g. AAC) although not in MP3. See for example http://www.stockis.se/AES112th_SBR.pdf
If you want to do any commercial work in this area, I highly recommend studying the patent situation carefully.  A massive amount of work has already been done in this field and since the license revenue is quite substantial, the work has been well protected by patents and there is incentive to enforce them.