AIR tools

AIR tools -- a MATLAB package of algebraic iterative reconstruction methods. We present a MATLAB package with implementations of several algebraic iterative reconstruction (AIR) methods for discretizations of inverse problems. These so-called row action methods rely on semi-convergence for achieving the necessary regularization of the problem. Two classes of methods are implemented: Algebraic reconstruction techniques and simultaneous iterative reconstruction techniques. In addition we provide a few simplified test problems from medical and seismic tomography. For each iterative method, a number of strategies are available for choosing the relaxation parameter and the stopping rule. The relaxation parameter can be fixed, or chosen adaptively in each iteration; in the former case we provide a new “training” algorithm that finds the optimal parameter for a given test problem. The stopping rules provided are the discrepancy principle, the monotone error rule, and the normalixed cumulative periodogram criterion; for the first two methods “training” can be used to find the optimal discrepancy parameter.


References in zbMATH (referenced in 12 articles )

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  1. Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj: Convergence analysis for column-action methods in image reconstruction (2017)
  2. Soltani, Sara; Andersen, Martin S.; Hansen, Per Christian: Tomographic image reconstruction using training images (2017)
  3. De Asmundis, Roberta; di Serafino, Daniela; Landi, Germana: On the regularizing behavior of the SDA and SDC gradient methods in the solution of linear ill-posed problems (2016)
  4. Jin, Qinian: Landweber-Kaczmarz method in Banach spaces with inexact inner solvers (2016)
  5. Nikazad, T.; Karimpour, M.: Controlling noise error in block iterative methods (2016)
  6. Soltani, Sara; Kilmer, Misha E.; Hansen, Per Christian: A tensor-based dictionary learning approach to tomographic image reconstruction (2016)
  7. Wei, Yimin; Xie, Pengpeng; Zhang, Liping: Tikhonov regularization and randomized GSVD (2016)
  8. Andersen, Martin S.; Hansen, Per Christian: Generalized row-action methods for tomographic imaging (2014)
  9. Seyyedi, Saeed; Cengiz, Kubra; Kamasak, Mustafa; Yildirim, Isa: An object-oriented simulator for 3D digital breast tomosynthesis imaging system (2013)
  10. Zhu, Zangen; Wahid, Khan; Babyn, Paul; Cooper, David; Pratt, Isaac; Carter, Yasmin: Improved compressed sensing-based algorithm for sparse-view CT image reconstruction (2013)
  11. Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj: Semiconvergence and relaxation parameters for projected SIRT algorithms (2012)
  12. Hansen, Per Christian; Saxild-Hansen, Maria: AIR tools -- a MATLAB package of algebraic iterative reconstruction methods (2012)