I use the same wallpaper for a long time now. But with high resolution displays, wallpaper started to look blurry and noisy, so I stopped using it.
But recently, my girlfriend reminded me of this great website which super-scales images using magic. Ok, not magic, but it uses "Deep Convolutional Neural Networks", which is pretty much the same thing. Results are amazing, try it yourself.
The best thing, website is free to use and project is opensource. Code is available on GitHub.
It supports max scaling of 2x, so if you need more you'll need to process image multiple times. Or you can dig in the code and add option for arbitrary scaling.
1 This is the resized image using waifu2x.Example #
Original, 250x250px jpeg 2
Result, 500x500px png
If you ask me, results are really impressive, kudos to nagadomi!