What you are trying to do is an interesting thing ...
I have an answer for your question, and some questions for you too.
My answer:
Yes, It is easy to do so. For that, you need to decide on the following:
1. What are you trying to do with this data (my question too) ?
2. Treating each pixel as Q4 element (2D) is possible and the most easy way (in my knowledge).
3. I assume that you know that FEM data lives on a quad or triangulated surface (in this case the image). if you want to consider each pixel as a Q4 element, the mesh is super super fine (actually very good or FEM process).
4. A very simple matlab script will do your job. Each corner of your pixel becomes a node (x and y coordinates), and the element connectivity is just what nodes make the pixel(here element) in counter clock wise notation (4 numbers in case of Q4 element).
5. the RGB data onthe nodes will become your unknown vector.
My questions:
1. what do you wish to do with FEM method with image data...
2. interpolate ? in side the pixel ... ?
3. in FEM procedures you usually solve for some unknowns. here what do you want to solve for in this case.