AIR tools II is a MATLAB-based package provides efficient, robust and flexible implementations of algebraic iterative reconstruction (AIR) methods for computing regularized solutions to discretize inverse problems, such as computed tomography. All methods are equipped with stopping rules, heuristics for computing a good relaxation parameter and several test problems from tomography. The package is intended for users who want to experiment with algebraic iterative methods and their convergence properties. The software is a much expanded and improved version of the package AIR Tools from 2012, based on a new modular design. In addition to improved performance and memory use, the platform offers more flexible iterative methods, a column-action method, new test problems, new demo functions and – perhaps most important – the ability to use function handles The package includes some of the most common Algebraic Iterative Reconstruction (AIR) methods, divided into three classes. (i) the algebraic reconstruction technique (ART)* based methods, that sequentially involves one row at a time, (ii) the column-action reconstruction technique (CART) based methods, that sequentially involve one column at a time also known as column-relaxation methods, and (iii) the simultaneous iterative reconstruction technique (SIRT) based methods, that simultaneously involve all the rows at a time, and therefore rely on matrix multiplications).
* The original algorithm is due to Kaczmarz; the name ART originates from the seminal paper by Gordon, Bender and Herman)