Tipard Video Converter got a bum rap in the comments today, as its noise removal and up-scaling were criticized, IMHO unfairly -- I'm Not saying that the converter from Tipard works wonders resizing or removing noise, but rather, no comparable app will do all that much better, if at all.
TO start with, when it comes to enlarging, Don't. When you work with video you're working with a string of still images that are more highly compressed than any still you're likely to ever see. And that's the really good quality stuff -- as the amount of compression increases, the amount [& size] of compression artifacts increases along with it. When you enlarge an image without AI, you're guessing as what colors the extra pixels should be -- the ones that you create out of thin air. When you enlarge video compression artifacts don't do well, at all.
That said, if you feel you must enlarge video, use software that at least gives you your choice of up-sizing algorithms -- one of the alternatives may very well [usually will] do better -- or use AI, which has a much better idea of what the subjects in your video are supposed to look like. If necessary convert the video to still images & batch process them in an image editing app, or look at video editors, or check out VapourSynth [or AviSynth]. Ffmpeg does not include those options, so neither do ffmpeg front ends, like most all converters. It's not that ffmpeg is lousy software, but the extra processing that you can get using something like AviSynth just isn't used anymore -- hasn't been really since analog bit the dust.
So what do you do if you want to watch a DVD? Buy a TV with at least decent up-scaling, and let the electronics do all the work -- designed for that make/model TV, they'll do better than most any software. Will you notice the difference in quality between a DVD & say a Blu-ray disc? Absolutely. But unless you use AI, if you go to the trouble of re-sizing & re-encoding that video you'll notice it too. If you want to see the video in its original quality, watch it at its original size, e.g. in a window on a PC/laptop or in a small window in the middle of your TV screen. Or if you're lucky, some company's remastered the original film for streaming or Blu-ray.
[Note: it is quite possible that in the future someone(s) will adapt the tech AMD &/or Nvidia have developed to upscale game display, and that might be a great, quick solution to enlarging video.]
Noise is a [Very] different animal. If you shot the video, noise could be created by the camera's electronics, similar to the noise you get with a digital camera, or it could be the result of the camera's encoding the video prior to storage. The best -- IMHO only pragmatic way -- to get rid of camera noise is with an AI app, same as with still images. To get rid of encoder induced noise [artifacts] use less or another type of video compression in the first place -- it's almost impossible to eliminate after the fact. And yes, that can mean getting/using a different camera. Encoding noise or artifacts are also present in most every DVD produced after the advent of Blu-ray, and it's there on purpose to give you an incentive or reason not to copy it.