I need to evaluate if the picture was resized (upscaled). Are there any approaches to that already? If not, what do you recommend me to start with?
As Raphael already said, in general it's impossible.
There is the field of image forensics where people look for methods to detect tampering with images. For JPEG images for example, there is a paper about detecting resizing: A new approach for JPEG resize and image splicing detection.
On the conceptual level, the task is clearly impossible: you won't be able to detect size changes of mono-coloured images. Patterns with only right angles will always be identical modulo dimensions as well.
So you need assumptions on the image and knowledge about the specific algorithm used for upscaling. Something may be possible for specific combinations, but it's impossible to tell in general.