GoKawiilUnlike CBS, you're unlikely to have $12 million to convert your videos to 4K. Home users converting video to 4K will instead have to choose between traditional interpolation or newer AI-based tools. Both methods will create the additional pixels needed to fill out an enlarged 4K frame, but not in the same way.
4K upscalers using interpolation rely on good, old-fashioned math. It takes a pixel from a single frame and looks at the color and brightness of the pixels around it. From there, it'll try to calculate how the pixels surrounding it will look. At a basic level, it might achieve this by sheer duplication, but more advanced algorithms will focus on trying to preserve edges and avoid jagged lines. The end result is pretty predictable, but one problem is softness. Interpolation can't magically recreate genuine detail or textures, making it seem slightly fake. Your TV might be able to do this automatically too, with varying degrees of success.
Luckily, AI upscaling looks to solve that problem. These models are trained on examples of low and high-resolution images that allow it to identify how common features should look on your screen. Instead of estimating each pixel, the AI is predicting what a sharper image will look like.
The result can be sharper and more convincing but, like interpolation, it won't be an exact match for the real world. AI upscalers can also introduce unusual artifacts that interpolation doesn't. AI models are constantly improving, however, so the quality and consistency you'll see today might seem antiquated in just a few years' time.
If you're working with older video, you may also need to think about interlacing, where video frames were split into two halves by odd and even horizontal lines, with each line refreshing each time the screen refreshes. Modern displays don't use interlacing, but older broadcasts meant for CRT-like screens would. Converting these kinds of videos will require you to de-interlace before upscaling, although how well you'll be able to upscale a 480i NTSC video to 4K in a way that maintains a watchable video quality is questionable.
Upscaling tools often feature plenty of configuration to help you get the result you want, whether it's using AI or interpolation. If a single pass through doesn't get you the result you're looking for, you can tweak the settings to have another go (as long as you've got the disk space).