I’m about to set up an image sitemap for SEO.
Each of my images is available in several different sizes (for mobile vs. desktop etc.), ranging from 400px to around 4000px wide.
Which resolution(s) should I submit in this sitemap, and why?
Only one version of the image should be included in your image sitemap. You can submit whichever size version you prefer, however, particularly when using common CMSes which auto-resize your images as required, this is usually the original version of the file which should be correctly sized as the largest version of the file required on your site.
If you are concerned about your high resolution images being accessible, you could choose to use the lower resolution versions in your image map. However, ideally in that situation you would still setup the image map with the full size version, but use image redirection (ie. server settings, plugins or htaccess) on your server to ward of file scraping.