I do a bit more than enlarge the pix that I enhance. An enhancement can go through 4-6 stages of processing through 3-5 pieces of imaging software. Some of the stages may be repeated several times. Enhancing can take 5-30 minutes per picture or capture.
First I enlarge them too big, remove image noise & compression distortion as much as possible. Then I sharpen them, which brings out more noise & distortion again, so I have to repeat the first process again, which dulls & blurs the image a little, so then I sharpen again. I can go through this cycle several times to clean up a picture. But do it too much, & the image starts to look cartoonish, or the subject starts too look over-processed, distorted or like an alien. And one never can get rid of all the distortion & artifacts without losing some of the image itself.
So it's impossible to get a perfect crystal clear picture out of a poor, blurry, distorted one, or real tiny ones. One could probably airbrush a photo too, to clean it up. But that would be even more time consuming. I don't want to add stuff to the original image, just enhance what's already there to make it look a little better.
After a bit of that processing, I send it through some edge detection software. It senses the edges of subjects & objects & makes them more defined, but push it too far & you'll actually lose some of the detail even though the edges are sharper.
Then I shrink the image back down to size that's pleasing to the eye & compress it with free Irfanview. For processing the image, I had previously blew it up way too far to ever look clear. After shrinking it back down to a size that looks crisper, & compressing it, some sharpness is lost. So I have to sharpen it again, which brings out more noise again, so I remove more image noise & distortion one more time.
If the original image wasn't too bad or was fair, the enhancements are a dramatic improvement, & the final image is a bit larger than the original, but also a considerable smaller file size. On very poor quality images or real tiny thumbnail-like ones, the enhancements only give a slight improvement, & are only slightly larger than the original. Or sometimes to make them as clear looking as possible, they may actually be smaller than the original to hide the poor quality & distortions in the image.
Except for free Irfanview software, the software & techniques I use to process & enhance images I made myself. I originally developed the processes to enhance blurry or small NASA, ESA, & astronomy images, or bring out strange stuff NASA airbrushed out of images that still remained faintly behind the airbrushing. One has to wonder if the ones who airbrushed out images for NASA deliberately didn't fully airbrush them because they didn't feel good about concealing so much from the public, so left just a trace behind that others can bring out with processing.
Indeed, there have been many NASA employees who have come forward to say that their job was just to airbrush stuff out of NASA photos or blur them all day, every day.
Anywho, many of the same enhancement techniques used on them, work good on pictures of people too.