In fact the Olympus implementation of this feature moves the sensor by half a photosite diagonally. They do it by re-purposing the existing in-body stabilization mechanism to move the sensor around.

User 'twic' posted a link to a very interesting article that describes this and also explains the difference between photosites and pixels:

https://chriseyrewalker.com/the-hi-res-mode-of-the-olympus-o...

Piezo actuators can make very fine movements. You can get positioning systems that can adjust position by nanometers, even sub-nm [1].

Also, cameras have had stabilization systems for a while now; I would assume they need similar pixel-scale precision. Some cameras shift the lens, some shift the sensor, but either way they need to shift the image-on-sensor by a very small amount, and also do it very rapidly.

[1] For example: https://www.pro-lite.co.uk/File/psj_piezoelectric_nanopositi...

Some projector manufacturers are shifting a 4K DMD around 4 times to increase the refresh rate of a 1080P image 4x.

All of them are shifting either by 4 or by 2 pixels you don’t have native 4K DMDs yet afaik.

There are some, but they're crazy expensive

Pentax did it with the K70 back in 2016.

They also did it earlier in 2015 with Pentax K-3 II. Also Olympus OM-D E-M5 Mark II had a similar feature in 2015.