If you can figure out, for each frame, which sets of (pre-aligned) pixels have been averaged, you can create a large system of equations that captures those relations and solve it to find the unblurred pixel values.

Depending on camera movement (and whether you might get "ground truth" information from pixels entering and leaving the areas near the borders) the system will be more or less well-conditioned. I'm going to try this for the data the author graciously provided and report back!