Journal of Computational and Applied Mathematics - Special issue: Applied computational inverse problems
Boundary conditions and multiple-image re-blurring: the LBT case
Journal of Computational and Applied Mathematics - Special issue: Applied computational inverse problems
Calculation scheme based on a weighted primitive: application to image processing transforms
EURASIP Journal on Applied Signal Processing
Acceleration methods for image restoration problem with different boundary conditions
Applied Numerical Mathematics
Stability of the notion of approximating class of sequences and applications
Journal of Computational and Applied Mathematics
Efficient minimization method for a generalized total variation functional
IEEE Transactions on Image Processing
New total variation regularized L1 model for image restoration
Digital Signal Processing
A note on algebraic multigrid methods for the discrete weighted Laplacian
Computers & Mathematics with Applications
Spectral Features and Asymptotic Properties for $g$-Circulants and $g$-Toeplitz Sequences
SIAM Journal on Matrix Analysis and Applications
Antireflective boundary conditions for deblurring problems
Journal of Electrical and Computer Engineering - Special issue on iterative signal processing in communications
Information Sciences: an International Journal
A note on the (regularizing) preconditioning of g-Toeplitz sequences via g-circulants
Journal of Computational and Applied Mathematics
Fast deconvolution with approximated PSF by RSTLS with antireflective boundary conditions
Journal of Computational and Applied Mathematics
Shift-invariant approximations of structured shift-variant blurring matrices
Numerical Algorithms
Extensions of the Justen---Ramlau blind deconvolution method
Advances in Computational Mathematics
A boundary condition based deconvolution framework for image deblurring
Journal of Computational and Applied Mathematics
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In a recent work Ng, Chan, and Tang introduced reflecting (Neumann) boundary conditions (BCs) for blurring models and proved that the resulting choice leads to fast algorithms for both deblurring and detecting the regularization parameters in the presence of noise. The key point is that Neumann BC matrices can be simultaneously diagonalized by the (fast) cosine transform DCT III. Here we propose antireflective BCs that can be related to $\tau$ structures, i.e., to the algebra of the matrices that can be simultaneously diagonalized by the (fast) sine transform DST I. We show that, in the generic case, this is a more natural modeling whose features are (a) a reduced analytical error since the zero (Dirichlet) BCs lead to discontinuity at the boundaries, the reflecting (Neumann) BCs lead to C0 continuity at the boundaries, while our proposal leads to C1 continuity at the boundaries; (b) fast numerical algorithms in real arithmetic for both deblurring and estimating regularization parameters. Finally, simple yet significant 1D and 2D numerical evidence is presented and discussed.