Insulate pipes in closet
If you simply boxed around it with 2x4s, insulated with fiberglass bat insulation, and covered with a double layer of drywall, it would give you quite a reduction in noise.  You will need to blank off that receptacle and leave an access panel in the front so the box is accessible.  

If you frame around it with metal studs, and use homasote rather than drywall, you will achieve even greater sound insulation.