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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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:1017-1398
1572-9265
1572-9265
DOI:10.1007/s11075-024-01960-3