One thing to remember: you cannot pull extra permission out of nowhere. When you enlarge the image, you can either have a blurry, smooth image, or have a sharp, blocky image, or you can have something in between. The best algorithms, which seem to have better performance with specific types of objects, make certain assumptions about the contents of the image, which, if true, can give higher apparent performance, but will be corrupted if these assumptions turn out to be false; there you trade precision for sharpness.
There are several good algorithms for scaling certain types of objects, including pixel art , faces, or text. More general algorithms for sharpening images include blurring masking, edge enhancement, and others, but they all imply specific things about the contents of the image, for example, that the image contains text or that the noisy area will still be noisy (or not) with higher resolution.
A low-resolution shelf-point or sandy sandy pattern will not work very well, and a computer can turn your seascape into something more like a mosh pit. Each scaling algorithm or sharpening filter has a number of costs associated with it.
For the right choice of scaling or sharpening algorithm, context, including sample images, is absolutely necessary.
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