Call of Duty: Ghosts will receive a day-one patch on PS4 which makes the campaign output at a native 1080p resolution. Otherwise, the output is 720p. As it stands presently, the multiplayer runs natively at 1080p but the single-player runs at 720p.
The patch will correct the issue which Activision said was a configuration issue.
"Call of Duty: Ghosts runs natively at 1080p on the PlayStation 4," an Activision spokesperson told Eurogamer. "There was a configuration issue in the retail version on single-player mode only. This has been addressed with a day one software update. People will be able to download the day one update when PlayStation 4 launches in their territory and play at native 1080p."
Without the day one update, you'll get the COD single-player upscaled, including the menu system and the HUD.