There are several ways of doing this in Photoshop.
You can, for instance, use Levels (ctrl+L) to lighten up the picture and you can mask out the underexposed area and lighten that up or you can use the dodge-tool with a light exposure-value.
However; your example picture can't be saved since it has too much noise in the dark area.
This means that there are limited amount of information for photoshop to get out, thus you can't achieve a good result.
Do you have any other examples?
M

rten - Wish you welcome