PPSSPP can run your PSP games on your PC in full HD resolution, and play them on Android too. It can even upscale textures that would otherwise be too blurry as they were made for the small screen of the original PSP.
Even on modern Android phones and tablets, you can often run at double the original resolution.
PPSSPP is an open source project, licensed under the GPL 2.0 (or later). Anyone is welcome to contribute improvements to the code. Partly thanks to such contributions, PPSSPP’s compatibility is steadily increasing, letting us all play our PSP games on the devices of our choice.