Creating a vaulted ceiling for patio

I just purchased a house that has a detached outdoor patio that has a vaulted roof (shingled) and a low flat ceiling. I thought that it would be much nicer to remove the flat ceiling and possibly create a vaulted ceiling or go with the exposed beam look. I have removed one of the 4X8 ceiling boards to see what it looks like above. There is one main large beam running dow the center of the ceiling with metal brackets on it and then long narrow beams running from the main beam to the edge of the covering every 2 feet that the ceiling boards are nailed to. Based on the attached pictures what is necessary to get rid of the low beams and create a much nicer vaulted ceiling? I also thought about just nailing plywood or hardy boards to the existing ceiling if the vaulted ceiling was too much of a hassle, but that would lower the ceiling further (although it would definately be a cleaner look than the roofing boards that are there now. Thanks in advance for your help.