AIR Tools - A MATLAB Package for Algebraic Iterative ...

Chapter 3
Iterative Methods for
Reconstruction
In this chapter we will give a brief introduction to the theory for some iterative
methods called SIRT and ART methods. The need for iterative methods arises,
when the dimensions of the matrix A become so large that direct factorization
methods become infeasible, which is usually the case in two and three dimensions.
This is typically the case when A is a discretization that arises from a
real-world problem. In this case one can use iterative methods instead of the
well-known Tikhonov regularization or TSVD described in section 2.3. Where
we for Tikhonov regularization have the regularization parameter ω, the number
of iterations k plays the role of regularization parameter for the iterative
methods.
In the following presented theory we will assume that all the elements in the
matrix A are nonnegative. In the articles where the methods are defined they
do not include used-defined weights, but we have chosen to include them in both
the description and the implementation.