This source gives a bit more information on the image:
"Battery K of the 1st Indiana Heavy Artillery Regiment, commanded by Captain Clayton Cox. This battery was located to the east of Fort Desperate, opposite to Priest Cap, and operated there throughout the siege
."
Here's a couple more from Port Hudson:
Capt. Edmund C. Bainbridge's Battery A, 1st U.S. Artillery, at the siege of Port Hudson, Louisiana, 1863. Bainbridge's Battery occupied a position northeast of Fort Desperate, about 400 yards from the fort's front. This battery of ten guns fired on the fort throughout the siege, and was responsible for the shell which destroyed one of the two guns available to Colonel Johnson on May 27th.
http://pth.thehardyparty.com/ft_desperate/pict&map_pages/bainbridge_battery.htm
Another photo of the 1st Indiana Heavy Artillery at Port Hudson. Possibly another battery but from the same artillery regiment.
Edit: Another photo, same location as the above image: