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Lectures on Numerical Analysis by Prof. Per Christian Hansen from DTU Compute, Technical University of Denmark:
Talk 2 "IR Tools: a Matlab Package with Iterative Regularization Methods for Inverse Problems"


IR Tools: a Matlab Package with Iterative Regularization Methods for Inverse Problems


Professor Per Christian Hansen
DTU Compute, Technical University of Denmark


15:30-16:30 / February 25th (Tuesday), 2020


National Center of Sciences Building, 2F, Medium Conference Room 3


We describe a new Matlab software package IR Tools with software for large-scale linear inverse problems.
The package serves two purposes: we provide implementations of a range of iterative solvers, including several recently proposed methods that are not available elsewhere, and we provide a set of large-scale test problems in the form of discretizations of 2D linear inverse problems.
The solvers include iterative regularization methods where the regularization is due to the semi-convergence of the iterations, and Tikhonov-type formulations where the regularization is due to a regularization term. In both cases, we can impose bound constraints on the computed solutions.
All the iterative methods are implemented in a very flexible fashion that allows the problem's coefficient matrix to be available as a (sparse) matrix, a function handle, or an object. The most basic call to all of the various iterative methods requires only this matrix and the right-hand side vector.
If the method uses any special stopping criteria, regularization parameters, etc., then default values are set automatically by the code. With an optional input structure, the user can also have full control of any of the algorithm parameters.
The test problems represent realistic large-scale problems found in image reconstruction and several other applications. These new test problems are meant to replace the small and outdated test problems from 1994 in Regularization Tools. The basic call to all of the test problem generators produces a matrix, a right-hand side and the corresponding exact solution. Similar to the iterative methods, the user can use an optional input structure to control specific features of the test problem.
We use numerical examples to illustrate the various algorithms and test problems available in this package.
This is joint work with Silvia Gazzola and James G. Nagy.


This lecture is supported by Invitational Fellowships for Research in Japan (Short-term S).
Scientific organizer: Kuniyoshi Abe (abe (at) gifu.shotoku.ac.jp)
Local organizer: Ken Hayami (hayami (at) nii.ac.jp)
Local organizer: Kensuke Aihara (aiharak (at) tcu.ac.jp)