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 97 articles )

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  1. Buccini, Alessandro: Fast alternating direction multipliers method by generalized Krylov subspaces (2022)
  2. Higham, Nicholas J.; Mikaitis, Mantas: Anymatrix: an extensible MATLAB matrix collection (2022)
  3. Huang, Guangxin; Liu, Yuanyuan; Yin, Feng: Tikhonov regularization with MTRSVD method for solving large-scale discrete ill-posed problems (2022)
  4. Hubmer, Simon; Ploier, Alexander; Ramlau, Ronny; Fosodeder, Peter; van Frank, Sandrine: A mathematical approach towards THz tomography for non-destructive imaging (2022)
  5. Lv, Zhonglu; Bao, Wendi; Li, Weiguo; Wang, Fang; Wu, Guoli: On extended Kaczmarz methods with random sampling and maximum-distance for solving large inconsistent linear systems (2022)
  6. Thong, Duong Viet; Gibali, Aviv; Vuong, Phan Tu: An explicit algorithm for solving monotone variational inequalities (2022)
  7. Wu, Wen-Ting: On two-subspace randomized extended Kaczmarz method for solving large linear least-squares problems (2022)
  8. Bangsgaard, Katrine O.; Andersen, Martin S.: A statistical reconstruction model for absorption CT with source uncertainty (2021)
  9. Brogaard Riis, Nicolai André; Dong, Yiqiu; Hansen, Per Christian: Computed tomography with view angle estimation using uncertainty quantification (2021)
  10. Cho, Taewon; Chung, Julianne; Jiang, Jiahua: Hybrid projection methods for large-scale inverse problems with mixed Gaussian priors (2021)
  11. Cipolla, Stefano; Donatelli, Marco; Durastante, Fabio: Regularization of inverse problems by an approximate matrix-function technique (2021)
  12. Dong, Yiqiu; Wu, Chunlin; Yan, Shi: A fast method for simultaneous reconstruction and segmentation in X-ray CT application (2021)
  13. Gazzola, Silvia; Nagy, James G.; Sabaté Landman, Malena: Iteratively reweighted FGMRES and FLSQR for sparse reconstruction (2021)
  14. Jakob S. Jørgensen, Evelina Ametova, Genoveva Burca, Gemma Fardell, Evangelos Papoutsellis, Edoardo Pasca, Kris Thielemans, Martin Turner, Ryan Warr, William R. B. Lionheart, Philip J. Withers: Core Imaging Library - Part I: a versatile Python framework for tomographic imaging (2021) arXiv
  15. Jiang, Jiahua; Chung, Julianne; de Sturler, Eric: Hybrid projection methods with recycling for inverse problems (2021)
  16. Jiang, Jiahua; Chung, Julianne; de Sturler, Eric: Hybrid projection methods with recycling for inverse problems (2021)
  17. Kang, Chuan-gang: Convergence rates of the Kaczmarz-Tanabe method for linear systems (2021)
  18. Kiefer, Lukas; Storath, Martin; Weinmann, Andreas: Iterative Potts minimization for the recovery of signals with discontinuities from indirect measurements: the multivariate case (2021)
  19. Liu, Yanli; Xu, Yunbei; Yin, Wotao: Acceleration of primal-dual methods by preconditioning and simple subproblem procedures (2021)
  20. Liu, Yong; Gu, Chuan-Qing: On greedy randomized block Kaczmarz method for consistent linear systems (2021)

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