**Introduction (Introduction to: Algebraic Image Reconstruction)**

The inverse Radon formulae have a great disadvantage, namely that the physical particle trajectories are simplified to ray paths. More precise (and more difficult) physics modelling would modify the underlying integral transforms (Radon and ray-) and we would need to develop completely new formalisms and inversion formulas.

Algebraic reconstruction techniques mean the solution of equation systems in matrix forms on discretized domains (spatial and sinogram). Improved physics modelling would then be simply a more accurate calculation of the matrix elements and formulation would not be affected at all. The solutions are usually iterative that can be based on algebraic or statistical considerations.

Firs we will show the construction of a discrete base.