Iterative methods for image deblurring: A Matlab object-oriented approach. In iterative image restoration methods, implementation of efficient matrix vector multiplication, and linear system solves for preconditioners, can be a tedious and time consuming process. Different blurring functions and boundary conditions often require implementing different data structures and algorithms. A complex set of computational methods is needed, each likely having different input parameters and calling sequences. This paper describes a set of Matlab tools that hide these complicated implementation details. Combining the powerful scientific computing and graphics capabilities in Matlab, with the ability to do object-oriented programming and operator overloading, results in a set of classes that is easy to use, and easily extensible.

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  1. Dykes, L.; Ramlau, Ronny; Reichel, L.; Soodhalter, K. M.; Wagner, R.: Lanczos-based fast blind deconvolution methods (2021)
  2. Jiang, Jiahua; Chung, Julianne; de Sturler, Eric: Hybrid projection methods with recycling for inverse problems (2021)
  3. di Serafino, Daniela; Landi, Germana; Viola, Marco: ACQUIRE: an inexact iteratively reweighted norm approach for TV-based Poisson image restoration (2020)
  4. Fung, Samy Wu; Tyrväinen, Sanna; Ruthotto, Lars; Haber, Eldad: ADMM-softmax: an ADMM approach for multinomial logistic regression (2020)
  5. Jia, Zhongxiao: The low rank approximations and Ritz values in LSQR for linear discrete ill-posed problem (2020)
  6. Jia, Zhongxiao: Approximation accuracy of the Krylov subspaces for linear discrete ill-posed problems (2020)
  7. 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)
  8. 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)
  9. Jia, Zhongxiao; Yang, Yanfei: A joint bidiagonalization based iterative algorithm for large scale general-form Tikhonov regularization (2020)
  10. Newman, Elizabeth; Kilmer, Misha E.: Nonnegative tensor patch dictionary approaches for image compression and deblurring applications (2020)
  11. Song, Xiongfeng; Xu, Wei; Hayami, Ken; Zheng, Ning: Secant variable projection method for solving nonnegative separable least squares problems (2020)
  12. Chung, Julianne; Gazzola, Silvia: Flexible Krylov methods for (\ell_p) regularization (2019)
  13. Aminikhah, Hossein; Yousefi, Mahsa: A special generalized HSS method for discrete ill-posed problems (2018)
  14. Cui, Jing-Jing; Peng, Guo-Hua; Lu, Quan; Huang, Zheng-Ge: Accelerated GNHSS iterative method for weighted Toeplitz regularized least-squares problems from image restoration (2018)
  15. Fan, Hong-Tao; Bastani, Mehdi; Zheng, Bing; Zhu, Xin-Yun: A class of upper and lower triangular splitting iteration methods for image restoration (2018)
  16. Kubínová, Marie; Nagy, James G.: Robust regression for mixed Poisson-Gaussian model (2018)
  17. Hnětynková, Iveta; Kubínová, Marie; Plešinger, Martin: Noise representation in residuals of LSQR, LSMR, and CRAIG regularization (2017)
  18. Renaut, Rosemary A.; Vatankhah, Saeed; Ardestani, Vahid E.: Hybrid and iteratively reweighted regularization by unbiased predictive risk and weighted GCV for projected systems (2017)
  19. Zhao, Xi-Le; Huang, Ting-Zhu; Gu, Xian-Ming; Deng, Liang-Jian: Vector extrapolation based Landweber method for discrete ill-posed problems (2017)
  20. Cai, Yuantao; Donatelli, Marco; Bianchi, Davide; Huang, Ting-Zhu: Regularization preconditioners for frame-based image deblurring with reduced boundary artifacts (2016)

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