Hero image woes and those things :)

As I am putting the final spin on a client's website, I am really lost on the best way to implement large images in the background for the website without losing clarity in the image. I've read several dated post on this topic, however, I am not clear as the idea dimensions. For example, on my client's website, click here in the header you will see that I have an image; however, the client says the image isn't clear which I don't know how to handle. For that section of the website, I took that image and created a 2000x600 pixel header space but as you see the picture is slightly blurred plus it's a close up where as the client wants to see more of the image and less of his head. Any advice?