Reversing Time Averaging and Reconstructing Extinction Rates with Approaches from Image Processing

In this paper, the relation between the extinction rate and the rate of last fossil occurrences as well as the relation between the fossil occurrence rate and the time averaged fossil occurrence rate is examined. Both relations are described by the same mathematical operation. This operation is commonly used in image processing, where it generates a blurring effect. Therefore the rate of last fossil occurrences can be taken as a blurred version of the extinction rate, and the time averaged fossil occurrence rate as a blurred version of the fossil occurrence rate. This connection has different applications. It allows to study the patterns different types of time averaging generate or the patterns of last fossil occurrences generated by different extinction rates. More importantly, it opens the possibility to use algorithms from image processing that reverse blurring effects for geological applications. This can be used to reverse the effects of time averaging or to reconstruct extinction rates from the rate of last fossil occurrences.