First of all, adjust your exposure time on your camera or reduce the light level. The image is horribly over exposed. Secondly try to make your lighting more uniform. You have a really bad hot spot in your image that cannot be solely attributed to lens shading. After that you should have a much better image to start with. Then you can try to further flatten the image by using background division. Take a blank shot and divide your image by the blank shot to correct for any remaining non-uniformities in lighting or lens shading.
See attached background correction example.
