Hi,
Such image would take 1.6 Gb in memory, even if it is split. So if the computer has loads of memory, that would be possible to have it in RAM. But that's not guaranteed a computer has so much memory.
So I would suggest to have a mechanism to load part of the image you need by splitting the image in tiles. For example, if it is a background that scrolls, the program can load the tiles that are visible. As you progress, the program can free the tiles are not visible anymore and load the new tiles.
If you need to display everything at the same time at a reduced size, then you would need to have prepared thumbnails. You can probably use imagemagick to prepare those thumbnails.