Suppose two instruments I0 and I1 measure the same quantity with the same resolution, where it is known that I0 is more reliable. The second, I1, is assumed a distortion of I0 in some sense. A statistical method is outlined where 1) the information from both I0 and I1 is combined to increase the reliability of I0 and 2) the distortion is quantified. An example is given in terms of shipborne precipitation radar and a spaceborne radiometer, both measuring rain rate.