SEAGATE FILE RECOVERY SOFTWARE SUITE FULL

It can extract a full image beforehand, but for a 4TB HDD it's quite a chore. TestDisk may be able to recover the former partition in-place, although it's quite risky.

R-Studio would be worth trying, it usually is very efficient at reconstructing a folder structure when the filesystem has been significantly altered (and can also do raw file recovery, targetting pretty much all common file formats). When the MFT has been completely overwritten (unlikely here after a quick format, and the recovery softwares wouldn't be able to recognize any folder structure whatsoever), the metadata is lost, meaning that the names, timestamps and other properties can not be recovered, even if the contents of all files are still 100% valid, in which case only raw recovery is possible. If you can recover files in raw modes, at least those files must be intact, their contents must be intact, but their records in the MFT may have been altered.

Space where former files used to be located being marked as free, system files can go wherever the system wants, most notably journaling files. Nothing has been written to the drive since the accidental format.ДЄt least on a Windows system, significant amounts of data can get overwritten even on a completely idle NTFS re-formatted HDD.

Seagate file recovery software suite