Speaker:
Marco Donatelli
Institution:
Università dell'Insubria, Como (Italy)
Time:
Friday, April 23, 2021 - 3:00pm to 4:00pm
Location:
Zoom (notice unusual day)
Zoom
We explore the use of a regularizing preconditioner for a modification of the linearized Bregman iteration applied to the image deblurring problem with a 1-norm regularization term in the wavelet domain. Motivated by the nonstationary preconditioned iteration introduced in [1] for least-square inverse problems, we propose a new algorithm that combines this method with the linearized Bregman algorithm [2]. The proposed preconditioning strategy improves the quality of the restored images and saves some computational cost with respect to the standard preconditioning employed in the modified linearized Bregman algorithm [3] and a numerical comparison with similar methods, like FISTA, is presented. We prove that it is a regularizing and convergent method. A variant with a structure preserving preconditioner is also considered [4].
Research partly carried out with D. Bianchi, A. Buccini, Y. Cai, M. Hanke, T.Z. Huang.
[1] M. Donatelli, M. Hanke, Fast nonstationary preconditioned iterative methods for ill-posed problems, with application to image deblurring, Inverse Problems, 29 (2013) 095008.
[2] Y. Cai, M. Donatelli, D. Bianchi, T.Z. Huang, Regularization preconditioners for frame-based image deblurring with reduced boundary artifacts, SIAM J. Sci. Comput., 38--1 (2016), pp. B164--B189.
[3] J.F. Cai, S. Osher, Z. Shen, Linearized {B}regman iterations for frame-based image deblurring, SIAM J. Imaging Sci., 2--1 (2009), pp. 226--252.
[4] D. Bianchi, A. Buccini, M. Donatelli, Structure Preserving Preconditioning for Frame-Based Image Deblurring, Springer INdAM Series, 36 (2019), pp. 33--49.
We explore the use of a regularizing preconditioner for a modification of the linearized Bregman iteration applied to the image deblurring problem with a 1-norm regularization term in the wavelet domain. Motivated by the nonstationary preconditioned iteration introduced in [1] for least-square inverse problems, we propose a new algorithm that combines this method with the linearized Bregman algorithm [2]. The proposed preconditioning strategy improves the quality of the restored images and saves some computational cost with respect to the standard preconditioning employed in the modified linearized Bregman algorithm [3] and a numerical comparison with similar methods, like FISTA, is presented. We prove that it is a regularizing and convergent method. A variant with a structure preserving preconditioner is also considered [4].
Research partly carried out with D. Bianchi, A. Buccini, Y. Cai, M. Hanke, T.Z. Huang.
[1] M. Donatelli, M. Hanke, Fast nonstationary preconditioned iterative methods for ill-posed problems, with application to image deblurring, Inverse Problems, 29 (2013) 095008.
[2] Y. Cai, M. Donatelli, D. Bianchi, T.Z. Huang, Regularization preconditioners for frame-based image deblurring with reduced boundary artifacts, SIAM J. Sci. Comput., 38--1 (2016), pp. B164--B189.
[3] J.F. Cai, S. Osher, Z. Shen, Linearized {B}regman iterations for frame-based image deblurring, SIAM J. Imaging Sci., 2--1 (2009), pp. 226--252.
[4] D. Bianchi, A. Buccini, M. Donatelli, Structure Preserving Preconditioning for Frame-Based Image Deblurring, Springer INdAM Series, 36 (2019), pp. 33--49.