Power your radio or scanner directly to your battery. Don't power it from the fuse panel or anywhere else. Don't ground it anywhere other than the battery. Note which side of the engine your alternator is on. Run the power wires under the hood on the opposite side of the engine. Get them as far away from the alternator as you can.
Go to RadioShack and grab some ferrite choke's. They're pretty cheap, 3 or 4 bucks for two, and install them on the power wires, right before they go into the back of the radio.
What's going on is, your alternator is making RF noise, and your power wires are acting as antennas and recieving it. You might not be able to get rid of the interference at all, or you might be able to nip it in the bud completely. Make sure you're using good quality coax as well, and inspect it to make sure it isn't knicked anywhere.