Not if that's all you have. The pixellation replaced the original pixels, it isn't a layer you can just remove. Having said that, I realized that the tools available to any CSI unit worth the television time would make this fix not only possible, but that it would take the tech no more than 10 seconds to achieve it.
In fact it has been done. I don't remember the specifics, but as I recall the news bite an international criminal was apprehended recently after the German police and intelligence services "de-pixellated" his pixellated digital image. Evidently extremely hi-tech and taking many moons to accomplish.
i remember hearing that they took a distorted image that was messed with in a photoshop-type program & "fixed" it. Pedophile I think. If it was a pixeliated image as in a zoom, I'm sure it could be fixed, but if you replace the entire nose with a solid color pixel the same size, I don't see how that can be fixed.
The German pedophile was an interesting case. The dude had posted a number of pictures of him self with a "pixilated" face to hide his identity. The pictures involved highly illegal (in Germany) activities with children. The police didn't create his face from a single pixilated image however, they patched it together from a large number of pixilated images. Since pixilation like this is typically random, if enough images are available, in the end all of them put together will contain enough information to "de-pixilate" the image.
If you squint your eyes and look at a pixilated image the pixilation almost seems to disappear. I'm wondering how a blur effect followed by a sharpening effect might work. If it's just a small portion of the clip you might try masking off just that area. Certainly won't look great but may be worth the experiment.
I tried my experiment on Happyfriar's image. Applied blur then tried to fix it with focus magic. The face looked better that the least pixelated version but unless the pixelated portion of your image is very small and only on screen for a few seconds, you would not like the results. And no, I didn't save the results.