Sometimes it is necessary to fuse data sets from different data sources in one data set. This fusion is called registration. But a problem is, that these data sets have different resolutions, different angles and different positions, so there are different approaches to achieve a good registration. The approach here ([3])  uses an information theoretic approch which bases on the Shannon information and can be applied on two data sets and provides good results for 3 data source combinations (MRI-MRA, MRI-CT, MRI-PET).
 

For the data registration the mutual information between the data sets is minimized. In order to speed up this process a simple 3 level pyramid is used. The first level contains the whole data, the second level only every second data point and the third level only every fourth data point. The mutual information is first optimized with the third, than the second and than the base level, which speeds up the registration with a factor of two.