The Kronecker product in approximation and fast transform generation
The Kronecker product in approximation and fast transform generation
Suppression of “salt and pepper” noise based on Youden designs
Information Sciences: an International Journal
SIAM Review
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
A Fast Algorithm for Deblurring Models with Neumann Boundary Conditions
SIAM Journal on Scientific Computing
Digital Image Restoration
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
Optimal Kronecker Product Approximation of Block Toeplitz Matrices
SIAM Journal on Matrix Analysis and Applications
A Note on Antireflective Boundary Conditions and Fast Deblurring Models
SIAM Journal on Scientific Computing
Kronecker Product Approximations for Image Restoration with Reflexive Boundary Conditions
SIAM Journal on Matrix Analysis and Applications
Deblurring Images: Matrices, Spectra, and Filtering (Fundamentals of Algorithms 3) (Fundamentals of Algorithms)
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
A new adaptive center weighted median filter for suppressing impulsive noise in images
Information Sciences: an International Journal
Deblurring Methods Using Antireflective Boundary Conditions
SIAM Journal on Scientific Computing
Information Sciences: an International Journal
Weighted and extended total variation for image restoration and decomposition
Pattern Recognition
Discrete Inverse Problems: Insight and Algorithms
Discrete Inverse Problems: Insight and Algorithms
Switching-based filter based on Dempster's combination rule for image processing
Information Sciences: an International Journal
An Efficient Iterative Approach for Large-Scale Separable Nonlinear Inverse Problems
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Journal of Mathematical Imaging and Vision
Fast computation of exact Zernike moments using cascaded digital filters
Information Sciences: an International Journal
On various eigen fuzzy sets and their application to image reconstruction
Information Sciences: an International Journal
Symmetric convolution and the discrete sine and cosine transforms
IEEE Transactions on Signal Processing
Reduction of boundary artifacts in image restoration
IEEE Transactions on Image Processing
Blur identification by the method of generalized cross-validation
IEEE Transactions on Image Processing
Iterative Shrinkage Approach to Restoration of Optical Imagery
IEEE Transactions on Image Processing
An Iterative Shrinkage Approach to Total-Variation Image Restoration
IEEE Transactions on Image Processing
A boundary condition based deconvolution framework for image deblurring
Journal of Computational and Applied Mathematics
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Reflexive boundary conditions (BCs) assume that the array values outside the viewable region are given by a symmetry of the array values inside. The reflection guarantees the continuity of the image. In fact, there are usually two choices for the symmetry: symmetry around the meshpoint and symmetry around the midpoint. The first is called whole-sample symmetry in signal and image processing, the second is half-sample. Many researchers have developed some fast algorithms for the problems of image restoration with the half-sample symmetric BCs over the years. However, little attention has been given to the whole-sample symmetric BCs. In this paper, we consider the use of the whole-sample symmetric boundary conditions in image restoration. The blurring matrices constructed from the point spread functions (PSFs) for the BCs have block Toeplitz-plus-PseudoHankel with Toeplitz-plus-PseudoHankel blocks structures. Recently, regardless of symmetric properties of the PSFs, a technique of Kronecker product approximations was successfully applied to restore images with the zero BCs, half-sample symmetric BCs and anti-reflexive BCs, respectively. All these results extend quite naturally to the whole-sample symmetric BCs, since the resulting matrices have similar structures. It is interesting to note that when the size of the true PSF is small, the computational complexity of the algorithm obtained for the Kronecker product approximation of the resulting matrix in this paper is very small. It is clear that in this case all calculations in the algorithm are implemented only at the upper left corner submatrices of the big matrices. Finally, detailed experimental results reporting the performance of the proposed algorithm are presented.