Finding Renditions for an Image via SharePoint REST API

In my application I'm displaying images via REST that I've pulled from a library using a query similar to this:

http://localhost/_api/web/GetFolderByServerRelativeUrl('/PublishingImages')/Files

As I'm iterating through the results, I'd like to determine somehow if there are any renditions for the image that have been created, and iterate/call the renditions as well. For this application I'd only have access to the SharePoint REST API (no CSOM or server-side abilities, basically stuck with $ajax()).

I could change the initial call to get me the folders in publishing images as well if needed.

So has anyone done renditions in the SharePoint 2013 REST API?