We present a survey of some iterative reconstruction methods for linear inverse problems that are based on the algebraic formulation of the problem, A x = b, such as ART and SIRT methods as well as methods based on Krylov subspaces. We survey the basic properties of these methods, discuss how and why they work, and demonstrate how to accelerate and stop the iterations. We also illustrate the use of these methods with hands-on MATLAB exercises, using existing implementations of these methods in the packages AIR Tools and Regularization Tools as well as pre-defined test problems.
The following links contain pdf-files with the slides and exercises and some additional MATLAB files necessary for this short-course.
The YouTube vidoes were recorded at School of Mathematics, Manchester University on Nov. 19-23, 2012, when I gave this course as part of the Manchester Image Reconstruction and Analysis (MIRAN) project. See the course plan (pdf file) for details of this course. Note that the slides have gone through minor revisions since then.
