IR Tools

IR Tools: A MATLAB Package of Iterative Regularization Methods and Large-Scale Test Problems. This paper describes a new MATLAB software package of iterative regularization methods and test problems for large-scale linear inverse problems. The software package, called IR Tools, serves two related purposes: we provide implementations of a range of iterative solvers, including several recently proposed methods that are not available elsewhere, and we provide a set of large-scale test problems in the form of discretizations of 2D linear inverse problems. The solvers include iterative regularization methods where the regularization is due to the semi-convergence of the iterations, Tikhonov-type formulations where the regularization is explicitly formulated in the form of a regularization term, and methods that can impose bound constraints on the computed solutions. All the iterative methods are implemented in a very flexible fashion that allows the problem’s coefficient matrix to be available as a (sparse) matrix, a function handle, or an object. The most basic call to all of the various iterative methods requires only this matrix and the right hand side vector; if the method uses any special stopping criteria, regularization parameters, etc., then default values are set automatically by the code. Moreover, through the use of an optional input structure, the user can also have full control of any of the algorithm parameters. The test problems represent realistic large-scale problems found in image reconstruction and several other applications. Numerical examples illustrate the various algorithms and test problems available in this package.


References in zbMATH (referenced in 39 articles , 2 standard articles )

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  1. Bai, Xianglan; Huang, Guang-Xin; Lei, Xiao-Jun; Reichel, Lothar; Yin, Feng: A novel modified TRSVD method for large-scale linear discrete ill-posed problems (2021)
  2. Buccini, Alessandro; Pasha, Mirjeta; Reichel, Lothar: Linearized Krylov subspace Bregman iteration with nonnegativity constraint (2021)
  3. Chen, Xiaotong; Herring, James L.; Nagy, James G.; Xi, Yuanzhe; Yu, Bo: An ADMM-LAP method for total variation myopic deconvolution of adaptive optics retinal images (2021)
  4. Cho, Taewon; Chung, Julianne; Jiang, Jiahua: Hybrid projection methods for large-scale inverse problems with mixed Gaussian priors (2021)
  5. Jiang, Jiahua; Chung, Julianne; de Sturler, Eric: Hybrid projection methods with recycling for inverse problems (2021)
  6. Luiken, Nick; van Leeuwen, Tristan: Relaxed regularization for linear inverse problems (2021)
  7. Nikazad, T.; Karimpour, M.: Column-oriented algebraic iterative methods for nonnegative constrained least squares problems (2021)
  8. Zhang, Hui; Dai, Hua: The regularizing properties of global GMRES for solving large-scale linear discrete ill-posed problems with several right-hand sides (2021)
  9. Buccini, Alessandro; Donatelli, Marco: A multigrid frame based method for image deblurring (2020)
  10. Buccini, A.; Pasha, M.; Reichel, L.: Modulus-based iterative methods for constrained (\ell_p)-(\ell_q) minimization (2020)
  11. Cornelis, Jeffrey; Vanroose, W.: Projected Newton method for noise constrained (\ell_p) regularization (2020)
  12. Cornelis, J.; Schenkels, N.; Vanroose, W.: Projected Newton method for noise constrained Tikhonov regularization (2020)
  13. Cueva, Evelyn; Courdurier, Matias; Osses, Axel; Castañeda, Victor; Palacios, Benjamin; Härtel, Steffen: Mathematical modeling for 2D light-sheet fluorescence microscopy image reconstruction (2020)
  14. Effland, Alexander; Kobler, Erich; Kunisch, Karl; Pock, Thomas: Variational networks: an optimal control approach to early stopping variational methods for image restoration (2020)
  15. Fung, Samy Wu; Tyrväinen, Sanna; Ruthotto, Lars; Haber, Eldad: ADMM-softmax: an ADMM approach for multinomial logistic regression (2020)
  16. 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)
  17. Gazzola, Silvia; Meng, Chang; Nagy, James G.: Krylov methods for low-rank regularization (2020)
  18. 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)
  19. Jia, Zhongxiao: Approximation accuracy of the Krylov subspaces for linear discrete ill-posed problems (2020)
  20. Jia, Zhongxiao: The low rank approximations and Ritz values in LSQR for linear discrete ill-posed problem (2020)

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