Flipped structured matrix-sequences in image deblurring with reflective and anti-reflective boundary conditions

Motivated by the recent work (Donatelli et al. Electron. Trans. Numer. Anal. 59 , 157-178 2023) on a preconditioned MINRES for flipped linear systems in imaging with Dirichlet boundary conditions (BCs), in this note we extend the scope of that research for including more precise BCs such as reflecti...

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Veröffentlicht in:	Numerical algorithms Jg. 100; H. 1; S. 277 - 309
Hauptverfasser:	Ferrari, Paola, Furci, Isabella, Serra-Capizzano, Stefano
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.09.2025 Springer Nature B.V
Schlagworte:	Algebra Algorithms Beräkningsvetenskap med inriktning mot numerisk analys Boundary conditions Computer Science Eigenvalue and singular value distributions Fourier transforms Ill-posedness and regularization problems Imaging and signal processing Krylov iterative methods Linear systems Localization Numeric Computing Numerical Analysis Reflective and anti-reflective BCs Regularization Scientific Computing with specialization in Numerical Analysis Spectrum analysis Structured matrices Theory of Computation 65F10 Imaging and signal processing 65F22 94A08 Krylov iterative methods Ill-posedness and regularization problems Eigenvalue and singular value distributions Reflective and anti-reflective BCs 65F15
ISSN:	1017-1398, 1572-9265, 1572-9265
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Abstract	Motivated by the recent work (Donatelli et al. Electron. Trans. Numer. Anal. 59 , 157-178 2023) on a preconditioned MINRES for flipped linear systems in imaging with Dirichlet boundary conditions (BCs), in this note we extend the scope of that research for including more precise BCs such as reflective and anti-reflective ones. We prove spectral results for the matrix-sequences associated to the original deblurring problem incorporating the considered BCs. More precisely, the resulting matrix-sequences are real quasi-symmetric i.e. real symmetric up to zero-distributed perturbations and this justifies the use of MINRES in the current setting. The theoretical spectral analysis is supported by a wide variety of numerical experiments, concerning the visualization of the spectra of the original matrices in various ways. We also report numerical tests regarding the convergence speed and regularization features of the associated GMRES and MINRES methods. Conclusions and open problems end the present study.
AbstractList	Motivated by the recent work (Donatelli et al. Electron. Trans. Numer. Anal. 59, 157-178 2023) on a preconditioned MINRES for flipped linear systems in imaging with Dirichlet boundary conditions (BCs), in this note we extend the scope of that research for including more precise BCs such as reflective and anti-reflective ones. We prove spectral results for the matrix-sequences associated to the original deblurring problem incorporating the considered BCs. More precisely, the resulting matrix-sequences are real quasi-symmetric i.e. real symmetric up to zero-distributed perturbations and this justifies the use of MINRES in the current setting. The theoretical spectral analysis is supported by a wide variety of numerical experiments, concerning the visualization of the spectra of the original matrices in various ways. We also report numerical tests regarding the convergence speed and regularization features of the associated GMRES and MINRES methods. Conclusions and open problems end the present study. Motivated by the recent work (Donatelli et al. Electron. Trans. Numer. Anal. 59 , 157-178 2023) on a preconditioned MINRES for flipped linear systems in imaging with Dirichlet boundary conditions (BCs), in this note we extend the scope of that research for including more precise BCs such as reflective and anti-reflective ones. We prove spectral results for the matrix-sequences associated to the original deblurring problem incorporating the considered BCs. More precisely, the resulting matrix-sequences are real quasi-symmetric i.e. real symmetric up to zero-distributed perturbations and this justifies the use of MINRES in the current setting. The theoretical spectral analysis is supported by a wide variety of numerical experiments, concerning the visualization of the spectra of the original matrices in various ways. We also report numerical tests regarding the convergence speed and regularization features of the associated GMRES and MINRES methods. Conclusions and open problems end the present study.
Author	Ferrari, Paola Serra-Capizzano, Stefano Furci, Isabella
Author_xml	– sequence: 1 givenname: Paola surname: Ferrari fullname: Ferrari, Paola organization: Department of Mathematics, University of Genoa, School of Mathematics and Natural Sciences, University of Wuppertal – sequence: 2 givenname: Isabella surname: Furci fullname: Furci, Isabella email: isabella.furci@unige.it organization: Department of Mathematics, University of Genoa – sequence: 3 givenname: Stefano surname: Serra-Capizzano fullname: Serra-Capizzano, Stefano organization: Department of Science and high Technology, University of Insubria, Division of Scientific Computing, Department of Information Technology, Uppsala University
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Cites_doi	10.1137/140974213 10.1016/S0024-3795(99)00251-7 10.1002/nla.2286 10.1137/23M1552498 10.1016/j.laa.2004.10.006 10.1007/978-3-319-23321-5_3 10.1007/s10092-008-0148-1 10.1016/j.cam.2013.05.018 10.1887/0750304359 10.1515/9780691213101 10.1137/05064607X 10.1007/s11075-018-0570-7 10.1007/978-3-319-53679-8 10.13001/ela.2021.5775 10.1137/1.9780898718874 10.1016/0024-3795(94)00025-5 10.1016/j.laa.2019.05.027 10.1016/S0024-3795(01)00335-4 10.1137/S1064827502410244 10.1109/TIP.2003.819861 10.1137/20M1379666 10.1553/etna_vol53s113 10.1007/s10543-018-0740-y 10.1137/S089547989427141X 10.1553/etna_vol58s177 10.1016/0165-1684(94)90067-1 10.1007/s00526-021-02128-w 10.1155/S1025583402000152 10.1093/oso/9780198504207.001.0001 10.1137/1.9780898718850 10.2352/ISSN.2470-1173.2018.13.IPAS-382 10.1137/S1064827598341384 10.1137/18M1207399 10.1007/s11075-023-01627-5 10.1553/etna_vol59s157 10.1016/j.exmath.2021.10.004 10.1137/0712047 10.1137/S0036144594276474 10.1007/978-1-4612-0653-8 10.1007/s11831-018-9295-y 10.1137/S1064827503421653 10.1553/etna_vol58s136 10.1002/nla.2137 10.1016/j.jat.2006.05.002 10.1137/23M1547251 10.1016/j.acha.2007.10.002 10.1016/j.cma.2016.05.042 10.1007/978-3-030-02233-4
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Snippet	Motivated by the recent work (Donatelli et al. Electron. Trans. Numer. Anal. 59 , 157-178 2023) on a preconditioned MINRES for flipped linear systems in... Motivated by the recent work (Donatelli et al. Electron. Trans. Numer. Anal. 59, 157-178 2023) on a preconditioned MINRES for flipped linear systems in imaging...
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SubjectTerms	Algebra Algorithms Beräkningsvetenskap med inriktning mot numerisk analys Boundary conditions Computer Science Eigenvalue and singular value distributions Fourier transforms Ill-posedness and regularization problems Imaging and signal processing Krylov iterative methods Linear systems Localization Numeric Computing Numerical Analysis Reflective and anti-reflective BCs Regularization Scientific Computing with specialization in Numerical Analysis Spectrum analysis Structured matrices Theory of Computation
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Title	Flipped structured matrix-sequences in image deblurring with reflective and anti-reflective boundary conditions
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