Some additional links I had.
See there more amazing upscaling pictures, and source code (for Tencent link above), and executables for Linux Windows, macOS (that you could use independently, or from Julia or the underlying C++ library, even on Android and iOS too):
Upscale 4x with ImageMagick Lanczo4 Filter
[vs]
Upscale 4x with realsr model=DF2K scale=4 tta=1
realsr-ncnn-vulkan.exe -i origin.jpg -o output.png -s 4 -x -m models-DF2K
“-resize 400%”, i.e. 4x may be standard terminology, or not, for 16x larger.
FYI: I also see the term “Extreme Super-Resolution” used, but I believe that’s the same magnification as above, as I do not really believe 16x16=256x magnification:
Abstract:
This paper reviews the NTIRE 2020 challenge on perceptual extreme super-resolution with focus on proposed solutions and results. The challenge task was to super-resolve an input image with a magnification factor ×16 based on a set of prior examples of low and corresponding high resolution images.
See also here, where you can compare 7 methods across several pictures:
Blind Super-Resolution Methods comparison
http://www.wisdom.weizmann.ac.il/~vision/kernelgan/resources/more_examples.html