The Eternal JPEG project was idealized because of this XKCD. The main idea consists of a JPEG image being tested against the effects of time.
Essentially, an image ought to be copied over and over around the Internet, without proper care for its intricacy. A screenshot may cause artifacts over time, and copying the image several times, straying further away from the original copy, can generate small data loss in the sample (although that normally happens because of compression, not errors in the copy "routine" itself). If the link to the XKCD above is still not dead, and if this website is still up, then you'll know what I mean.
And such is the base for this project, the idea of an image, being shared around, copied, but without the data loss. The idea is to not allow the original image to die out (be it because of the all sources to it being lost, or because of data loss itself), for as long as it is possible.
It is relatively simple to keep the image intact, but to be sure the image is still a 1:1 copy of the original, there has to be a way to verify its integrity, this could be done with signatures or checksums of the original sample of the project. As the objective of the project is count how long it is possible to keep the matrix sample around, some mechanism to count the time elapsed since the image was taken should be also used, this could range from a timestamp in the image's metadata, or simply a mark in the image itself. There has to be some care regarding time measurement, timezones and even leap seconds can alter the definitive timestamp, so something like the Unix timestamp should probably be used.
A reliable image format must be used, as they might end up being phased out as time goes on and technology changes. The image on this website must also not be trusted as the original at all times, and multiple copies should be kept, in case of bits flipping because of cosmic rays, or even the original source being taken down. The data that follows the image must also not be lost (the timestamp and checksum, for example), for they are just as important as the image itself.