I read something about this or a very similar project. The idea is to create a camera with several modern camera sensors that, with the appropriate lenses, will look at the same region where Alpha century is located. They supposedly will make this as small as possible and pay to get it lunched into space. Cutting the red tape should make this possible, working out there that is a different question.
Most of the expense that institutions, such as Nasa have, is the testing and re-testing of the equipment to ensure that it will work in space. All this also makes that projects, such as Hubble, end up being lunched with 8 or 10 year old technology, and even then did not work at first.
My point is, I don't think that private enterprises will ever get enough money to successfully lunch a project like this and have working successfully.