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 50 articles )

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  1. Benvenuto, Federico; Jin, Bangti: A parameter choice rule for Tikhonov regularization based on predictive risk (2020)
  2. Lei, Yunwen; Zhou, Ding-Xuan: Convergence of online mirror descent (2020)
  3. Wu, Nianci; Xiang, Hua: Projected randomized Kaczmarz methods (2020)
  4. Censor, Yair; Heaton, Howard; Schulte, Reinhard: Derivative-free superiorization with component-wise perturbations (2019)
  5. Gazzola, Silvia; Hansen, Per Christian; Nagy, James G.: IR tools: a MATLAB package of iterative regularization methods and large-scale test problems (2019)
  6. Gibali, Aviv; Mai, Dang Thi; Vinh, Nguyen The: A new relaxed CQ algorithm for solving split feasibility problems in Hilbert spaces and its applications (2019)
  7. Hansen, Per Christian; Dong, Yiqiu; Abe, Kuniyoshi: Hybrid enriched bidiagonalization for discrete ill-posed problems. (2019)
  8. Heaton, Howard; Censor, Yair: Asynchronous sequential inertial iterations for common fixed points problems with an application to linear systems (2019)
  9. Hu, Yunyi; Andersen, Martin S.; Nagy, James G.: Spectral computed tomography with linearization and preconditioning (2019)
  10. Hu, Yunyi; Nagy, James G.; Zhang, Jianjun; Andersen, Martin S.: Nonlinear optimization for mixed attenuation polyenergetic image reconstruction (2019)
  11. Schöpfer, Frank; Lorenz, Dirk A.: Linear convergence of the randomized sparse Kaczmarz method (2019)
  12. Zhang, Jian-Jun: A new greedy Kaczmarz algorithm for the solution of very large linear systems (2019)
  13. Zhong, Min; Wang, Wei; Jin, Qinian: Regularization of inverse problems by two-point gradient methods in Banach spaces (2019)
  14. Bazán, Fermín S. V.; Boos, Everton: Schultz matrix iteration based method for stable solution of discrete ill-posed problems (2018)
  15. Bubba, T. A.; Labate, D.; Zanghirati, G.; Bonettini, S.: Shearlet-based regularized reconstruction in region-of-interest computed tomography (2018)
  16. Elfving, Tommy; Hansen, Per Christian: Unmatched projector/backprojector pairs: perturbation and convergence analysis (2018)
  17. Hansen, Per Christian; Jørgensen, Jakob Sauer: AIR tools II: algebraic iterative reconstruction methods, improved implementation (2018)
  18. Jia, Zhongxiao; Yang, Yanfei: Modified truncated randomized singular value decomposition (MTRSVD) algorithms for large scale discrete ill-posed problems with general-form regularization (2018)
  19. Kazantsev, Daniil; Jørgensen, Jakob S.; Andersen, Martin S.; Lionheart, William R. B.; Lee, Peter D.; Withers, Philip J.: Joint image reconstruction method with correlative multi-channel prior for x-ray spectral computed tomography (2018)
  20. Lei, Yunwen; Zhou, Ding-Xuan: Learning theory of randomized sparse Kaczmarz method (2018)

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