In some internet forums, the extundelete tool is often recommended to rescue data from a harddrive. I have tested out the tool, but it struggles for a LVM2 logical container which is the standard in Fedora Linux. The better idea is to use the photorec tool.
1. dd bs=4M if=/dev/partition of=backup.img
2. sudo photorec backup.img
The good news is, that the photorec is recognizing an .img file which contains of a LVM2 volume easily. Then, the user has to specify in the option menu on which harddrive he likes to store all the recovered data and then it will take many hours until the workflow is complete. The directory is populated with many files which are recovered by the software. Right now, the photorec tool is the most advanced program in the Internet fur such a purpose. According to the documentation it is working also with NTFS drives from Windows, but i have only tried out to recover data from a ext4 drive with a lvm2 volume.
The only disadvantage is, that the date/time is not correct of the file, so it's a bit complicated to identify to the correct file. Also all the directory names are gone. But it's better than nothing