How to calculate Noise and distortion of an image?
You should do it on a known set of calibration targets. For example, this type of calibration target is being used to measure noise. You should find the patches locations, and measure the noise by some metric. If you don't know any metric, you can start by browsing DXOlabs site, or Imatest site.

I guess that you mean radial distortion. Radial distortion can be found by a process called camera calibration, by using a known target such as checkerboard. For more info, see Camera Calibration Toolbox. Here is an image from another software that does it:

I didn't understand your question at all. Please reprase it and add more information.