However, you can only do this if you know the @nickname of the user you want to expand. You must also select the View option from the menu. If you do this you will be able to see the actual resolution of the photo but you will not be able to save it.
However, you can enlarge the image in the Photos app as long as you take the pixelation factor into account. If you're using a Windows phone, you'll need to find a third-party editor. This is because the default editor does not offer a 4:5 option.
There are several other third-party applications that can also perform the same feat. Some of the best are complex and require you to change iPhones settings. Others do the same but are not free. You can also download the Instagram profile picture viewer to view a photo or video without revealing the identity of the users.