I actually came up with a sweeper concept where a large box container with one end open and reinforced walls go around scooping up space junk, compacting it, and then directing it either to the moon or out of orbit back to earth as a compacted mass. Could be any size, though large enough for an average satellite I think would be best.
The University of Arizona (UA) is heavily involved in space junk research, primarily through its Space4 Center.