Reducing noice, improving contrast, increasing resolution

Given an image, can we reduce the noise? Yes, denoising is a commonly available tool. We can denoise the image, usually at the expense of resolution. Most denoising algorithms inevitably smoothen. Given an image, can we improve the contrast? Yes, through edge detection and sharpening. Where pixel values jump, we can exaggerate the difference and make the gradient even higher. Given an image, can we increase the resolution? For pixel graphics, no! Even if we upsample, say, from 256×256 to 512×512, we won’t be able to recover information which was never there in the original 256×256 image.