Clever image zooming. What to write in PaintEvent?

[ModeZt]

Hello. I'm making a simple image (geographic map) editor for myself.
1) I have a QScrollArea and a custom Widget inserted into the scroll area.
2) I have a large image. 5000x5000 pixels. I read it into a QPixmap.
3) I have a second qpixmap. i put a scaled copy of my image into that pixmap.
in the paintevent of the widget i draw the second pixmap.

The problem is a huge memory usage. For example if i whant a 200% zoom i make a doubled copy of my image and store it in memory together with the original image..

Maybe there's a way to write a more efficient PaintEvent?
Thx.