I'm pretty sure this is not possible with any permutation of the thumbnail URL. I don't think there is any relationship between the thumbnail name and the original's name. The thumbnail is called "Billy" and the full image is called "Peter". There's no relationship between the two to my knowledge.
Furthermore, if you have the thumbnails stored, it's not even a foregone conclusion that the original images still exist at their original location. Nor will the API be helpful doing a reverse image search.
The best you can do (to my knowledge) is attempt to scrape a reverse image search based on the thumbnail. This will in the majority of cases -- but certainly not all cases -- give you the large image URL. But only if the original image still exists. (Of course, scraping Google is a violation of TOS... so be aware of the downsides)
http://skyzerblogger.blogspot.jp/2013/01/google-reverse-image-search-scraping.html