You can use this Firefox plugin to download any image using the context menu and it will use (online) Waifu2xBooru to upscale the image and then compress it to jpg or png to your computer.
This extension is a web extension built for Firefox 45+. It is different than the older versions.
Go to the releases, select the newest version and download the xpi file. Upon download you should be prompt to install the extension.
Using the current version has no xpi file yet because it is still early but can be used on newer versions of Firefox. Download the source and go to about:debugging and choose the manifest.json file to load the extension into the browser. This is technically for debugging so you have to re-add it every time you close your browser. This is work in progress until I actually submit it in the future.
Images on Waifu2xBoou can only save images max of 3840 x 3840 or 5mb.
Current version will save all images as jpeg (choice later).
Any images under the area of 1280x720 pixels will only upscale once using Waifu2x to preserve image quality. There are only max 2 upscales per image. Images with transparency will also work!
The source engine this uses is https://waifu2x.booru.pics/.
git clone https://github.com/matthewn4444/Waifu2x-Image-Saver.git
Thanks to the people who created Waifu2x and pica and FileSaver.js make this extension.