Please try everything else recommended here first. If/when that doesn't work the nuclear option may be Meguiars Hot Wheels Chrome Cleaner. It's the over the counter version of Meguiars pro-level heavy duty wheel cleaner.
The stuff is seriously strong and you'll want to make sure you use it outside, don't let it get on your skin, and DO NOT let it dwell for very long. Spray it on, agitate, and rinse it off quickly.
A few years ago I bought a set of competition wheels second hand. I'm confident the previous owner had never washed them in the short time he owned them. They were black with brake dust and there were a few small areas like you show where the dust had baked into the paint. I tried other wheel cleaners, tar remover, and possibly some full strength APC. Nothing would get rid of of the dust on those spots. The Hot Wheels Chrome Cleaner wiped it out with little/no effort.
Again, it's a product of last resort and you have to be very careful, but it might work where nothing else will. I haven't used it since that day, but keep the bottle around just in case.