In this paper the basis of PET (Positron Emission Tomography) is
reviewed, and it is shown that the measured signals can be modelled as the
Radon transform of the desired spatial distribution of, e.g., the
brain activity.

Next, two of the direct reconstruction methods are presented. Both are
derived from inversion of the Radon transform. It is shown that the
reconstruction can be based on filtering and integration techniques.

Another major class of reconstruction techniques is presented,
namely the linear algebra based methods, which often are formed as
iterative methods. A very fast way of implementing a set of iterative
reconstruction techniques is shown along with a set of examples.