This map on Veteran can be tough, I don't want to imagine what it's like on Elite.
I never worry about silenced weapons on this level because I generally try to go through quick to get the POW's. I first arm Alpha with a sniper, then arm bravo with two M4's and a M249. I use the sniper to take out the watchtower guards and the perimeter. I avoid the back of the compound until I get the POW's.
Once my sniper finishes with the outside I position him at the far watchtower in Recon in the prone position. The enemies won't see him and he won't feel tempted to shoot anyone. I then take control of Bravo, and take them through the first watchtower through that area with the buildings, and get ready at the next tower. I then retake control of my sniper, shoot the two guards next to the POW's take Bravo over and make a mad dash for the POW's while Alpha attempts to cover me. Once I've rescued the POW's, I get some cover, hunker down and assault until it's safe. Then I take Bravo, clear the hospital get Moroshokin (spelling?) and head outside. I'll send Alpha with his sniper rifle to clear those guys patrolling near the extraction zone and make a mad dash to the extraction.
This always works for me but everyones style is different.