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 59 articles )

Showing results 1 to 20 of 59.
Sorted by year (citations)

1 2 3 next

  1. Behling, Roger; Bello-Cruz, J.-Yunier; Santos, Luiz-Rafael: The block-wise circumcentered-reflection method (2020)
  2. Benvenuto, Federico; Jin, Bangti: A parameter choice rule for Tikhonov regularization based on predictive risk (2020)
  3. Cueva, Evelyn; Courdurier, Matias; Osses, Axel; Castañeda, Victor; Palacios, Benjamin; Härtel, Steffen: Mathematical modeling for 2D light-sheet fluorescence microscopy image reconstruction (2020)
  4. Gazzola, Silvia; Kilmer, Misha E.; Nagy, James G.; Semerci, Oguz; Miller, Eric L.: An inner-outer iterative method for edge preservation in image restoration and reconstruction (2020)
  5. Jia, Zhongxiao: Regularization properties of Krylov iterative solvers CGME and LSMR for linear discrete ill-posed problems with an application to truncated randomized SVDs (2020)
  6. Lei, Yunwen; Zhou, Ding-Xuan: Convergence of online mirror descent (2020)
  7. Webber, James W.; Quinto, Eric Todd: Microlocal analysis of a Compton tomography problem (2020)
  8. Webber, James W.; Quinto, Eric Todd; Miller, Eric L.: A joint reconstruction and lambda tomography regularization technique for energy-resolved x-ray imaging (2020)
  9. Wu, Nianci; Xiang, Hua: Projected randomized Kaczmarz methods (2020)
  10. Censor, Yair; Heaton, Howard; Schulte, Reinhard: Derivative-free superiorization with component-wise perturbations (2019)
  11. Dong, Yiqiu; Hansen, Per Christian; Hochstenbach, Michiel E.; Brogaard Riis, Nicolai André: Fixing nonconvergence of algebraic iterative reconstruction with an unmatched backprojector (2019)
  12. Gazzola, Silvia; Hansen, Per Christian; Nagy, James G.: IR tools: a MATLAB package of iterative regularization methods and large-scale test problems (2019)
  13. 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)
  14. Hansen, Per Christian; Dong, Yiqiu; Abe, Kuniyoshi: Hybrid enriched bidiagonalization for discrete ill-posed problems. (2019)
  15. Heaton, Howard; Censor, Yair: Asynchronous sequential inertial iterations for common fixed points problems with an application to linear systems (2019)
  16. Hu, Yunyi; Andersen, Martin S.; Nagy, James G.: Spectral computed tomography with linearization and preconditioning (2019)
  17. Hu, Yunyi; Nagy, James G.; Zhang, Jianjun; Andersen, Martin S.: Nonlinear optimization for mixed attenuation polyenergetic image reconstruction (2019)
  18. Schöpfer, Frank; Lorenz, Dirk A.: Linear convergence of the randomized sparse Kaczmarz method (2019)
  19. Soubies, Emmanuel; Soulez, Ferréol; McCann, Michael T.; Pham, Thanh-an; Donati, Laurène; Debarre, Thomas; Sage, Daniel; Unser, Michael: Pocket guide to solve inverse problems with GlobalBioim (2019)
  20. Zhang, Jian-Jun: A new greedy Kaczmarz algorithm for the solution of very large linear systems (2019)

1 2 3 next