If it's a static image you only have to load once, then there isn't much optimization to attempt aside from possibly loading only one portion at a time as needed. But don't attempt that until you've actually tried loading the whole thing at once and found it to be too slow. I've loaded 1080p textures in SFML before without any noticeable delay, so I doubt there's any need to do this for 2048.
For the scrolling part, use views. One of the official tutorials discusses that.