I will begin by explaining various aspects about image resizing: how it works, what the important problems are, who would be interested in this. I’ll continue by comparing several existing methods. Finally I’ll conclude with the best method to use.
How does enlarging work?
Upsizing an image increases its resolution (size in pixels/points). To do this, information from the original image is used to create the enlarged version. Imagine a grid of pixels in a plane. In the original image they are all side by side. Enlarging the image means enlarging the grid. The more you stretch it, the more separated the pixels become. Those pixels in-between need to be filled-in. This is called interpolation. There can be other steps after interpolation.
Problems that need to be solved by upsizing
One of the problems that appear is that for small images pixels on the edges may be aliased. This becomes more apparent when enlarging. This is the jagged edges problem that many upsizing methods try to overcome. In one extreme you have edges that are sharp but jagged in another smooth but blurry. A compromise between smoothing an edge and keeping it sharp is searched for. Over-smoothing to maintain sharpness is not that hard to obtain but this creates an unrealistic look to images. Another problem is loss of detailed texture in the upsized image. The only method that even considers this is reshading.
When is upsizing an image useful?
Increasing the size by 200% means transforming a 3 megapixel (MP) image into a 12 MP one. If something like this can be created without losing quality then using an average camera and upsizing it would be almost the same as using a professional camera. Also, cropping and enlarging a portion of an image would be equivalent to having a better zoom lens on your camera. Of course, taking the photo with a professional camera and upsizing it would make very large prints easy.
Well known methods for enlarging an image
I’ll present a few widely known approaches. Some are commercially available: Photoshop, Genuine fractals, Photo zoom and others are free: Reshade.
Photoshop
Although everybody considers Photoshop as The tool of choice for any image manipulation, its features cover only some basic needs in this field. It is mainly designed to be a framework for image processing by allowing the inclusion of plug-ins that can easily interoperate. Because of this, even experienced Photoshop users have a hard time when upsizing images. The default algorithms for this purpose are made to be fast but not very powerful.
Best methods for upsizing images
These methods go further in their search for better quality upsizing. They are designed to allow greater enlargement factors without serious degradation in image quality.
Reshade
This is the newest method from the ones I mentioned. It permits enlargements of up to 200% without losing any quality. This means that even an experienced photographer would have a hard time picking an enlarged version from an original photo. Beyond this zoom factor, the images look a little over-processed. Even at higher zoom ratios reshade seams to work better on most images than any of the other techniques. From my point of view it's the best choice. I wouldn’t need greater zooming anyway because the degradation becomes visible with any possible technique beyond 200% enlargement.
Genuine fractals
This method tries not to overdo the edge sharpening and de-blurring like Photo zoom and maintains the quality of the image pretty good (for zoom factors of about 500%). For smaller zooms the image quality is very similar to what you can get in Photoshop. That means a lot of blurry edges remain after upsizing.
Photo zoom
Although the clarity of the edges is better than for Genuine fractals (at large zoom factors, 400%), there is an obvious smoothing effect that creates the impression that the image has been over-painted. This might be ok if it’s what you’re looking for but for photography, it adds an unrealistic look to the resized images. Although small details when enlarged remain smooth, reshading does a better job at this, also keeping them small.
Conclusion
In conclusion, I do not suggest using enlarging for every photo you take. The original can always look better even if an enlarged version has insignificant quality loss. But, it often happens that you want to crop only a part of a picture and it becomes too small to print or use as desktop wallpaper. Or maybe you don’t have your best camera nearby and use a lower megapixel one. In these situations enlarging becomes the best option available. I recommend reshading your pictures for best quality. It’s also freely available online at: reshade.com.
Computers 
