A prolific inventor who has battled the Patent and Trademark Office for decades will get three computer video processing patents from applications filed back in 1995.

The patent office had argued inventor Gilbert P. Hyatt wasn’t entitled to the patents because he unreasonably delayed the processing of his applications. But the U.S. District Court for the District of Columbia rejected that argument, known as prosecution laches, saying the patent office caused much of the delay and didn’t try to speed...