 <p>You cannot generally retrieve missing information.</p> <p>If you know what it is an image of, in this case a Gaussian or Airy profile then it's probably an out of focus image of a point source - you can determine the characteristics of the point.</p> <p>Another technique is to try and determine the character tics of the blurring - especially if you have many images form the same blurred system. Then iteratively create a possible source image, blur it by that convolution and compare it to the blurred image.<br> This is the general technique used to make radio astronomy source maps (images) and was used for the flawed Hubble Space Telescope images</p>