Dear Nick,
Realistically, the easiest and fastest way to do this is to manually edit the images in a bitmap programme, selecting the background and making it transparent. Then save the result as a .png file. Don’t use .jpg, as they can't contain transparency information.
If using OS X, you can get very good results with images like the one you posted just with the “instant alpha” tool in the free Preview app bundled with the system.
In PsychoPy/Python you can create masks to do this programmatically with varying degrees of sophistication, complexity and difficulty, but the result of just selecting pixels on the basis of colour will likely be quite poor. That is the approach taken by the ancient .gif format which has only 8 bit colour, but with 24 bit jpgs, you’ll be surprised how many non-white white pixels there are, and you may get quite poor performance, particularly on the edges. That is what something like instant alpha tools give you: nicely blended edges.
You might have some joy though: check the “face_jpg.py” Coder demo which uses an image like yours as its own mask, with no need to do anything computational.
Regards,
Michael