Can I recover files deleted from an app in iTunes>MyIPad->File Sharing?

I am using Stop Motion Studio on my iPad. When I export a project I use iTunes and copy the .stopmotionmobile file from the File Sharing tab, after selecting my device and the Stop Motion Studio App. I thought that the files on that directory were ONLY the files I was exporting, so when I was done I deleted all of them. The files are in fact ALL the files used by St.Mo.St so I infact deleted ALL my stop motion projects. I can't see anyway to recover these files...can any one assists

Image below shows where I deleted the files from. I have since added the files that are there and realized the .stopmotion ones are the projects in the application. There are 15 or so more of those that I deleted that I'd like to recover.