The first thing you need to do is get him checked by a vet to rule out any hearing or neurological issues!
Then you could bring in a trainer.... personally I would use my trusty water bottle [or a small water pistol] here.
In the house when he barks, stand somewhere he can't see you....aim and fire, then walk in to the room, give the command 'QUIET' in a firm voice give the command 'BED' or put him on to a down position and then and only then praise and treat him. Rinse and repeat lol
You can carry the water bottle out on a walk too and at the first bark, aim fire, command 'QUIET' .... Oh I'm sure you can work the rest out.
A muzzle will only [excuse the pun' mask the behaviour, also if you think the water bottle is too harsh, try looking up Victoria Stillwell as she will have training techniques for this too.
Lisa x