If you have a custom login screen image on your Mac (the image that shows as the desktop before anyone logs in) it's likely to get removed and replaced with a very blurry default image each time you update your OS. It seems like each new version of Mac OS X/macOS stores the login image in a different place, breaking any customization with each update.
Fortunately setting a new custom login screen is easy. And it has the added benefit of removing the extreme blur effect that Sierra likes to use.
This is the most important step because macOS Sierra is really picky about what it will accept as the login desktop. If your new login image is the wrong size or format it will simply disappear, replaced with a very blurry default desktop image.
You need a png file that is 1920 pixels wide and 1080 pixels high. Nothing else will work.
The easiest way to create such a file is to open a high resolution image (one larger than 1920×1080 pixels) in Photoshop and...
Your image is now ready to act as your new login artwork.
It's worth noting that macOS is not going to add any blur effect using this method, so if you want your login artwork to appear blurry (presumably to obscure details from someone looking at the Mac while it was locked) you'll need to add the blur effect yourself. Generally the easiest time to do thesis between steps 5 and 6 above. Choose Filter > Blur > Gaussian Blur... and then adjust the slider until you like the amount of blur.
macOS Sierra looks for login screen artwork of a certain size/format in a specific place. Now that you have the correct size/format you just need to get it into the right place.
In the finder choose Go > Go To Folder... and enter the text /Library/Caches . It should look exactly like this:
In there you are likely to find two items, but we only care about the one called com.apple.desktop.admin.png. That is the one we need to replace. You can see it here.
Drag the existing com.apple.desktop.admin.png file to the trash. Option-Drag (this is important, we want to move a copy of your new file) your new login screen artwork from the desktop into the place it previously held.
Choose the Apple icon in the top left and select Log Out. That should take you back to the login screen. If the previous steps worked you will see your new, non-blurred artwork in place.
If you see anything else, usually an extremely blurry generic desktop type image, it means that macOS Sierra did not like your new image file – either the size for format was wrong. It will have deleted it and put a new image in place – this is why we moved a copy into the Cache folder, not the original.
Check the size and format of your file and try again.