If you're looking for software where it might be possible to "substantiate the trustworthiness of the software" you might consider using PhotoRec (part of the
testdisk software). It's source code is available to browse, and it's also in the Debian & Ubuntu (linux distros) repositories, and has been for years. Photorec was originally designed to recover lost photos from memory cards (so I read somewhere) but it can also recover a ton of other filetypes from lots of different filesystems. It runs on Linux, Windows, Mac...
About recovering photos from your phone, as others mentioned if they were on a memory card then taking it out & reading it on a computer would be the easiest. If it were on internal memory, that would be harder, but might be possible if your phone can enable "USB mass storage mode" for the area that held the photos...
Your Samsung could have Android 4 to 4.4, so these instructions from the PhotoRec FAQ might help:
If you want to recover data from a memory card used in your phone, put the card in an USB card reader. To recover files from an internal memory, you have to enable the USB mass storage mode.
ie. Samsung Galaxy S2/S3 or Nexus, HTC Desire X/V/C, HTC One X/V/S, LG
Optimus L5/7/9, Optimus G, Motorola Droid RAZR, Sony Xperia V/T,
Kindle Fire HD
- Open the Setting > More
- Search then Tap on USB utilities
- Check the option: Connect Storage to PC
Then plug the USB cable into the device and connect to your computer.
The USB connected screen with the large green Android icon will
appear. Tap on Connect USB storage. A confirmation dialog box will
appear. Tap OK. The green Android icon will turn orange, indicating
that the phone is now in USB Mass Storage mode and should now appear
as USB disk drives in Devices with Removable Storage
ie. Nexus 4, Google Nexus 10, Samsung Galaxy S4
- Go to Settings -> About Phone/Tablet.
- Go to “Build Number” at the end of the Scroll list.
- Tap on “Build Number” repeatedly 7 times (Yes, it's not a typo)
- Now Developer Option will be included in setting list of yours now. Go to “Develop Options” to check USB debugging > OK. Done.
Then you can use PhotoRec on the now accessible drive/partition.
You might be able to copy the entire filesystem from your Android device, then dig through it with PhotoRec / Testdisk, or a similar tool looking for photos, deleted or not. That would involve using ADB (Android Debug Bridge), and might need a rooted device. Some guides are here: