Direct recovery will not be possible. A clue lies in the description; “permanent deletion” clearly implies that the deletion is irreversible, you’ll not find a “permanently deleted” file in your deleted folder.
If the deleted file is included in a device backup, such as iCloud or iTunes, you may be able restore your device to its state at the time of the backup:
Restore your iPhone, iPad or iPod touch from a backup – Apple Support
If entertaining the option to restore from backup, consider first that the items within the the backup will be determined by your backup settings at the time the backup was created/updated. Also consider that any changes to data or files that have occurred since the last backup will be lost during the restore process.
An alternative approach might be to simply re-download the media file, if still available, from its source.