You could try some polishing/restoring cream that might work on some of the oxidization. It though depends how deep to the lacquer it has spread. I use those polishing creams (and elbow grease) all the time to old frames and it really brings the shine back and takes away a lot of the surface damages.
At least it would be a cheap alternative to try out before full on lacquer removal and frame polishing work!
If the blemishes or blooms are only in the lacquer then you can carefully cut this back with fine wet & dry (try 1200) then clear coat over the top.
This is relatively easy, but it’s time consuming.. the more time you take the better it will look, you could test a small area away from the graphics first.
Be very careful over the graphics not to ‘cut’ through.
Before you do the whole thing, cut back the lacquer somewhere not too visible and test spray the clear coat.
A spray can of a less aggressive paint like clear Acrylic should do the job.
The whole bike will need a fine cut, even the un-blemished bits so that the clear coat can get a key otherwise it could de-laminate.
**EDIT** as Hamster says, if it's corrosion in the alloy, it's a complete strip down. :cry:
That looks like oxidized aluminum. You'll want to strip the frame and start researching the best way to remove it. Unfortunately aluminum oxide is harder than aluminum. So you'll want to be careful. Once that's done though, can't recommend mother's polish enough.
It's a problem with all polished alluminium. As a metal, It basically starts to corrode the second its cut or exposed to air. That's why it's a bitch to weld. If you decide to re lacquer the frame, it needs to be clean and done asap after polishing and de greasing. However, the reality is it will fail in time, especially if it's not sprayed in a very controlled environment. I personally dont bother, instead in the past I have lightly oiled the frame with acf50 or akin and then re polish whenever you like.