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 19 articles )

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  1. Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj: Convergence analysis for column-action methods in image reconstruction (2017)
  2. Gazzola, Silvia; Wiaux, Yves: Fast nonnegative least squares through flexible Krylov subspaces (2017)
  3. Hnětynková, Iveta; Kubínová, Marie; Plešinger, Martin: Noise representation in residuals of LSQR, LSMR, and CRAIG regularization (2017)
  4. Jiao, Yuling; Jin, Qinian; Lu, Xiliang; Wang, Weijie: Preconditioned alternating direction method of multipliers for inverse problems with constraints (2017)
  5. Nikazad, Touraj; Abbasi, Mokhtar; Elfving, Tommy: Error minimizing relaxation strategies in Landweber and Kaczmarz type iterations (2017)
  6. Soltani, Sara; Andersen, Martin S.; Hansen, Per Christian: Tomographic image reconstruction using training images (2017)
  7. Tang, Yu Chao; Zhu, Chuan Xi; Wen, Meng; Peng, Ji Gen: A splitting primal-dual proximity algorithm for solving composite optimization problems (2017)
  8. 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)
  9. Jin, Qinian: Landweber-Kaczmarz method in Banach spaces with inexact inner solvers (2016)
  10. Nikazad, T.; Karimpour, M.: Controlling noise error in block iterative methods (2016)
  11. Soltani, Sara; Kilmer, Misha E.; Hansen, Per Christian: A tensor-based dictionary learning approach to tomographic image reconstruction (2016)
  12. Wei, Yimin; Xie, Pengpeng; Zhang, Liping: Tikhonov regularization and randomized GSVD (2016)
  13. Jørgensen, Jakob S.; Sidky, Emil Y.; Hansen, Per Christian; Pan, Xiaochuan: Empirical average-case relation between undersampling and sparsity in X-ray CT (2015)
  14. Jørgensen, J.S.; Kruschel, C.; Lorenz, D.A.: Testable uniqueness conditions for empirical assessment of undersampling levels in total variation-regularized X-ray CT (2015)
  15. Andersen, Martin S.; Hansen, Per Christian: Generalized row-action methods for tomographic imaging (2014)
  16. Seyyedi, Saeed; Cengiz, Kubra; Kamasak, Mustafa; Yildirim, Isa: An object-oriented simulator for 3D digital breast tomosynthesis imaging system (2013)
  17. Zhu, Zangen; Wahid, Khan; Babyn, Paul; Cooper, David; Pratt, Isaac; Carter, Yasmin: Improved compressed sensing-based algorithm for sparse-view CT image reconstruction (2013)
  18. Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj: Semiconvergence and relaxation parameters for projected SIRT algorithms (2012)
  19. Hansen, Per Christian; Saxild-Hansen, Maria: AIR tools -- a MATLAB package of algebraic iterative reconstruction methods (2012)