The question is a legal one, and as with all legal questions the answer is, "It depends."
Peter Kuran was able to claim copyright on Trinity and Beyond. That's classified as "restoration," and that's copyrightable. Applying creative techniques to enhance source material and correcting the effects of age is intellectual property. Of course Kuran also produced original material to explain and dramatically frame his source footage, so the question of copyright on the entire opus doesn't really present a legal difficulty. But, for example, if you were to use his cleaned-up and enhanced footage of nuclear-device tests he would have a strong copyright claim against you.
You have taken public domain material and applied various commonly-available tools to produce a cleaned-up, interpolated version. You're adding material to what was there, which was created by you, and modifying the existing material according to decisions that you make on how to apply the tools. That's creative content, and you are entitled to claim copyright in it. The question, "by what measure?" is best answered by stating to what degree you applied expertise or artistic/aesthetic judgment in producing the final result.
The bar you have to clear in order to be an "author" as far as copyright goes is fairly low. Someone defending an infringement claim you might bring, on the grounds that you have merely repackaged public-domain content, would have to show that the process by which you produced your version was so inconsequential and automatic that it amounted to nothing creative. I haven't yet looked at the tools, so I have no informed opinion for how much skill it takes to operate them, or what creative choices are possible. But in general, any substantial transformation you make to public domain material is copyrightable if there is a chance that someone else can make similar choices differently. For example, Mark Gray is able to claim copyright on many of his Spacecraft Films DVDs because he has edited them into a convenient volumes. Editions of public-domain material can receive a whole-work copyright on the edition, even if everything that contributed to the edition was originally public domain. Selecting what is or isn't in your edition is authorship as copyright defines it.
The counterargument is that all you have done is to make public-domain material more useful and appealing toward the purposes for which the original material would have been sought. Commercial uptake of source material for commercially-exploitable purposes is one of the reasons we like having public-domain material be freely, non-exclusively usable. We want creators to be able to say, "I don't have the talent or energy to produce new content entirely on my own, but I can do something creative and useful using this other thing as a jumping-off point." And one of the chronic impediments to this is the difficulty in obtaining high-quality versions of public-domain material. The exceptions to copyright such as Fair Use and public domain are meant to speak to the larger issue of protecting creativity in general. That is, a court will balance allegations of infringement against the value of allowing the particular use case to the general climate of creativity. It is conceivable that a court could rule that, despite the effort you put in, you've merely contributed to making public-domain material more suitable for the kind of reuse it was intended for.
My personal, non-lawyer opinion is that the pro-authorship argument is stronger. The creative, editorial effort required to produce high-quality renditions of already-existing materials probably qualifies as a copyrightable transformation. If you really need to know, you need an IP lawyer. And sadly they're often quite expensive. They require extra training because they need a degree not only in law but also in the field the intellectual property comes from -- here, image processing and artificial intelligence.
