This is kind of ironic, because about a month ago I found a wounded tired pigeon in my backyard. This one was solid white, clean looking and huge. I noticed he had a tag on his leg and I was able to get close enough to get his ID
# from it. I got online and tracked down his owner and it turned out he was a certified thoroughbred racing pigeon that went off course. His owner said he was launched from Illinios for a race to Detroit. Apparently they had problems with solar-flares which apparently can throw off the birds' built-in sense of direction. All I had to do was catch it, feed it and water it for about 4 days, then let it go. By then he had his strength back up and took off for home.
As for your pigeon, I don't know if I'd want to try to catch a wild bird. I know around here, we have a people that will come out and get it. They specialize in capturing wounded wild birds and nursing them back to health, but they usually do this for birds of prey like hawks and eagles. Maybe you could look for something like that?