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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Vydáno v:	Numerical algorithms Ročník 100; číslo 1; s. 277 - 309
Hlavní autoři:	Ferrari, Paola, Furci, Isabella, Serra-Capizzano, Stefano
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.09.2025 Springer Nature B.V
Témata:	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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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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