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 28 articles , 2 standard articles )

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  1. Buccini, Alessandro; Donatelli, Marco: A multigrid frame based method for image deblurring (2020)
  2. Buccini, A.; Pasha, M.; Reichel, L.: Modulus-based iterative methods for constrained (\ell_p)-(\ell_q) minimization (2020)
  3. Cornelis, Jeffrey; Vanroose, W.: Projected Newton method for noise constrained (\ell_p) regularization (2020)
  4. Cueva, Evelyn; Courdurier, Matias; Osses, Axel; Castañeda, Victor; Palacios, Benjamin; Härtel, Steffen: Mathematical modeling for 2D light-sheet fluorescence microscopy image reconstruction (2020)
  5. Effland, Alexander; Kobler, Erich; Kunisch, Karl; Pock, Thomas: Variational networks: an optimal control approach to early stopping variational methods for image restoration (2020)
  6. Fung, Samy Wu; Tyrväinen, Sanna; Ruthotto, Lars; Haber, Eldad: ADMM-softmax: an ADMM approach for multinomial logistic regression (2020)
  7. 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)
  8. Jia, Zhongxiao: Regularization properties of LSQR for linear discrete ill-posed problems in the multiple singular value case and best, near best and general low rank approximations (2020)
  9. 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)
  10. Jia, Zhongxiao: Approximation accuracy of the Krylov subspaces for linear discrete ill-posed problems (2020)
  11. Jia, Zhongxiao; Yang, Yanfei: A joint bidiagonalization based iterative algorithm for large scale general-form Tikhonov regularization (2020)
  12. Kindermann, Stefan; Raik, Kemal: A simplified L-curve method as error estimator (2020)
  13. Webber, James W.; Quinto, Eric Todd: Microlocal analysis of a Compton tomography problem (2020)
  14. Zhang, Liping; Wei, Yimin: Randomized core reduction for discrete ill-posed problem (2020)
  15. Caruso, Noe; Michelangeli, Alessandro; Novati, Paolo: On Krylov solutions to infinite-dimensional inverse linear problems (2019)
  16. Chung, Julianne; Gazzola, Silvia: Flexible Krylov methods for (\ell_p) regularization (2019)
  17. Gazzola, Silvia; Hansen, Per Christian; Nagy, James G.: IR tools: a MATLAB package of iterative regularization methods and large-scale test problems (2019)
  18. Gazzola, Silvia; Noschese, Silvia; Novati, Paolo; Reichel, Lothar: Arnoldi decomposition, GMRES, and preconditioning for linear discrete ill-posed problems (2019)
  19. Gazzola, Silvia; Sabaté Landman, Malena: Flexible GMRES for total variation regularization (2019)
  20. Hansen, Per Christian; Dong, Yiqiu; Abe, Kuniyoshi: Hybrid enriched bidiagonalization for discrete ill-posed problems. (2019)

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