Did you have iCloud photo library turned on? If so, just go to iCloud.com and sign in to see if there is anything saved under photos. If not, do you have a "photo stream" folder in your photos? If you've just restored your device, connect to WiFi and see if anything appears in that folder.
If the above doesn't give you any results, then without a backup there isn't really an easy way to recover what you've lost. You will need to enquire with data recovery experts to see if they can do anything.