Ok, I didn't realize how many people had this problem but I managed to get rid of it completely.
I had the high pitched noise at startup, lasted about 15 seconds or so and faded away. Every time the radio powered on, whether the vehicle was started or not. One thing I did during my troubleshooting was connect the radio directly to the battery with a speaker connected to it. It did not hum, hiss, make a high pitched noise or anything else. It was perfect. This confirmed to me that the radio itself was fine.
This drove me nuts for days. In my particular situation, I had a Metra/Axxess interface to keep Onstar/chimes/etc. The Metra interface had speaker level inputs and did NOT convert them to low level output for the factory Bose amp. I called Metra and they informed me that they no longer convert the signal because they claim most newer factory amps can accept high level inputs.
I was skeptical so I purchased a cheap Scosche level converter. Went out of the radio with the speaker wires to the Scosche and then to the Metra inputs. It removed the high pitched noise, and also removed a constant hum (like you would hear if someone had the volume turned to max with no audio playing). Radio played absolutely perfect after that. I think, at least in my case, that the factory amp was getting such a ridiculously overpowered input, it was picking up normally undetectable sounds from the radio. I'm guessing maybe the cd drive spinning up to check for a disc, maybe the case fan in the back of the unit spinning up, could've been anything. But that's how I fixed mine.
I guess it depends if you have a factory amp. Hopefully this will help.