Its easier to understand if you just ignore the term "retina", which is a marketing term that has no real definition, like "high fidelity".
Generally speaking, there really is no way to increase resolution. You can change the native resolution of an image by rescaling it to a different resolution, but if the target resolution is higher, the effective resolution (the resolution you perceive) will still be stuck at the original resolution, and even just slightly lower due to scaling artifacts. If it were possible to do this, all of the TV shows shot on SD videotape in the 80's and 90's would be available in HD by now. It's not, and they aren't, with the noticeable exception of programs originally shot in higher resolution such as film, and then retelecined to HD. When your local CW affiliate runs an old 1997 episode of Friends, that is exactly what happens; a SD-resolution sub-master is rescaled to full 1080i for broadcast. And it still appears to viewers as if it were in SD, because originally, it was.
This barrier applies to all pixel-based or bit-mapped content. Raster-based stuff such as most modern fonts, can be scaled without these issues and maintain full resolution over a large range, because these images are based in being rerscaled on the fly in math, typically from bezier formulas. Pictures, not so much, unless you have access to a higher-rez original or the raw file.
Of course if you are a tech in the fantasy land of NCIS or CSI, there is software available to make that fuzzzy license plate from 3 blocks away crystal clear when blown up by a factor of 10,000, or apparently so, and it seems to be something they can pull out of the toolkit on a daily basis. The black ops areas of the government aren't talking, but odds are that even the most sophisticated software can't really do that, except on a pretty rudimentary level. But check back in a few years; If someone told me I would be able to watch a movie instantly on a device half the size of a legal pad 10 years ago, I would have given them that same exact advice then: check back in a few years.
Affordable software might be able to improve things, but not by much. Of course if you live in that TV fantasy land, everything that happens on a computer is accompanied by annoying little beeps and boops and clicking noises that never happen in the real world, so that just serves as another reminder that to buy in to any of this we have to fully suspend disbelief, and that in reality none of this is really possible.
To guarantee the highest resolution and quality, you have to start with the highest resolution and quality, and then do everything possible to preserve that through all iterations and workflows. Once resolution is reduced, it generally stays reduced and it is very difficult if not impossible to do much to put it back together again, even with full assistance from all the king's horses and all the king's men.