Woodruff's brother, David, told ABC News staffers in an e-mail Thursday his brother's doctors in Bethesda, Md., "are optimistic about his recovery," the New York Post reported.
"Bob's amazing team of doctors, nurses and corpsmen continue to be pleased with the progress he makes each day," the e-mail said. "The more we learn about Bob's injuries, the more we appreciate just how lucky he is.
"We need to remind ourselves it's only been 2 1/2 weeks since he sustained his injuries in Iraq. We live in a world of instant gratification, where patience as a virtue is rarely practiced. Our family now has a whole new appreciation for the word and what it truly means to be patient."
While Woodruff remains hospitalized under sedation, cameraman Doug Vogt is now receiving outpatient treatment, The Post said.