Dieback and rebirth of Wisteria

I have a 13 year old Wisteria, that until last year was glorious and has been flowering for many years. Last year there were many flowers in May but not many leaves, compared to normal. Then before the summer was over all of the leaves were gone, and it looked like it had died. This year there are some fresh shoots comping from the base of the plant, but the rest of the established wood looks dead. My question is should I cut back all of the old, what appears dead, wood, and effectively start again with this new birth of the plant?