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 79 articles )

Showing results 1 to 20 of 79.
Sorted by year (citations)

1 2 3 4 next

  1. Bangsgaard, Katrine O.; Andersen, Martin S.: A statistical reconstruction model for absorption CT with source uncertainty (2021)
  2. Brogaard Riis, Nicolai André; Dong, Yiqiu; Hansen, Per Christian: Computed tomography with view angle estimation using uncertainty quantification (2021)
  3. Cho, Taewon; Chung, Julianne; Jiang, Jiahua: Hybrid projection methods for large-scale inverse problems with mixed Gaussian priors (2021)
  4. 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
  5. Jiang, Jiahua; Chung, Julianne; de Sturler, Eric: Hybrid projection methods with recycling for inverse problems (2021)
  6. Kang, Chuan-gang: Convergence rates of the Kaczmarz-Tanabe method for linear systems (2021)
  7. Kiefer, Lukas; Storath, Martin; Weinmann, Andreas: Iterative Potts minimization for the recovery of signals with discontinuities from indirect measurements: the multivariate case (2021)
  8. Liu, Yanli; Xu, Yunbei; Yin, Wotao: Acceleration of primal-dual methods by preconditioning and simple subproblem procedures (2021)
  9. Liu, Yong; Gu, Chuan-Qing: On greedy randomized block Kaczmarz method for consistent linear systems (2021)
  10. Liu, Yong; Jiang, Xiang-Long; Gu, Chuan-Qing: On maximum residual block and two-step Gauss-Seidel algorithms for linear least-squares problems (2021)
  11. Luiken, Nick; van Leeuwen, Tristan: Relaxed regularization for linear inverse problems (2021)
  12. Nikazad, T.; Karimpour, M.: Column-oriented algebraic iterative methods for nonnegative constrained least squares problems (2021)
  13. Steinerberger, Stefan: Surrounding the solution of a linear system of equations from all sides (2021)
  14. van Lith, Bart S.; Hansen, Per Christian; Hochstenbach, Michiel E.: A twin error gauge for Kaczmarz’s iterations (2021)
  15. Behling, Roger; Bello-Cruz, J.-Yunier; Santos, Luiz-Rafael: The block-wise circumcentered-reflection method (2020)
  16. Benvenuto, Federico; Jin, Bangti: A parameter choice rule for Tikhonov regularization based on predictive risk (2020)
  17. Cornelis, J.; Schenkels, N.; Vanroose, W.: Projected Newton method for noise constrained Tikhonov regularization (2020)
  18. Cueva, Evelyn; Courdurier, Matias; Osses, Axel; Castañeda, Victor; Palacios, Benjamin; Härtel, Steffen: Mathematical modeling for 2D light-sheet fluorescence microscopy image reconstruction (2020)
  19. Dong, Yiqiu; Schönlieb, Carola-Bibiane: Tomographic reconstruction with spatially varying parameter selection (2020)
  20. 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)

1 2 3 4 next