The first method, known as the filtered back projection method, is based on the Radon transform and therefore requires that the data are collected as parallel beam projections. It is a fast algorithm and the most widely used in today's commercial systems.
Attenuation is difficult to handle in an exact way for the filtered back projection method.
In this project, we used a post-processing operation known as Chang's method to correct for attenuation. There are, however, pre-processing techniques as well for attenuation compensation in this algorithm. The second method used in this project was an algebraic technique which is more general and can handle a large class of geometries, including fan beam projections. This method formulates the reconstruction problem in terms of a set of linear equations, and is closely related to image restoration techniques. In fact, modifying only the constraints under which the reconstruction equations are solved, one can implement, e.g., an expectation maximization algorithm.