I don't think this is actually ghosting - Ghosting implies a fainter offset signal due to limitations of the graphics card or monitor, it looks more like a problem with the redraw rate - for example using a very slow display driver - like a slow, generic Frame Buffer driver rather then something appropriate for your card.
Compiz is for "3d" and fancy stuff (Transparency jumps to mind), and requires graphics acceleration to work well. The solution is to find an appropriate driver for your graphics card and install it (and how you do that will depend on your graphics card). The correct driver makes differences of orders-of-magnitude.