Vice grips would probably work best. I can't tell how big the bolt is, but the large size vice grips (locking pliers) could be carefully clamped on end and the bolt unscrewed. Large Vice grips have knurled jaw tips and grip very tightly, enough to crush that bolt head.
Maybe put a few layers of duct tape on the wood to protect it beforehand. Be careful and the bolt will come out with no damage.
A brute force method, with high wood damage potential would be to file two flats on the bolt head and use a wrench to remove it. One slip filing, even with duct tape and your wood could be gouged.