I found all that vector stuff confusing. Even found software to do it, but it was out of my range.
I was tasked by a friend to do a poster for her husband's birthday. They gave me some photos I scanned at 300 dpi, but others they had scanned themselves at 72, or 100.
I opened up a new background on PhotoShop at 300dpi and the poster size I wanted, I think it was 20x30.
I cleaned off the background on all the pictures so I just had the head shot. Some of these pictures were from the 1950s and 60s that they had scanned themselves and not at a very high resolution. I took these cleaned head shots and dragged them into my poster sized background. I enlarged the photos to whatever size I wanted. When I finished and flattened image, sepia toned it, sent it to Wal-Mart (I'm all about cheap and free). The resulting poster had no pixilation what so ever.
The picture looked as good as the original 1x1 inch photo.
How it happened is above my understanding. That I can do it and I've tested it with all kinds of pictures, is what matters to me. But you are right. If the image is pixilated to begin with, then it will stay that way, but the ones I got, they look good at 1", and they stayed looking good at 10".
To me, that is magic I can work with.
I'll leave the mathematical calculations to those who like numbers.
All I can say is to the inquiring minds to give my process a try and see if his results are what they want.
As long as at least a few people succeed, then my advice has paid off.
Luv you XOXOXOXOXO