A Fast MAP Algorithm for High-Resolution Image Reconstruction with Multisensors
Multidimensional Systems and Signal Processing
Super-Resolution Image Restoration from Blurred Low-Resolution Images
Journal of Mathematical Imaging and Vision
Recursive filtering of images with symmetric extension
Signal Processing
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
Minimization of a Detail-Preserving Regularization Functional for Impulse Noise Removal
Journal of Mathematical Imaging and Vision
Stabilization of explicit methods for convection diffusion equations by discrete mollification
Computers & Mathematics with Applications
Acceleration methods for image restoration problem with different boundary conditions
Applied Numerical Mathematics
Approximation BFGS methods for nonlinear image restoration
Journal of Computational and Applied Mathematics
Blind motion deblurring using multiple images
Journal of Computational Physics
An Edge-Preserving Multilevel Method for Deblurring, Denoising, and Segmentation
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
An Adaptive Method for Recovering Image from Mixed Noisy Data
International Journal of Computer Vision
An empirical identification method of Gaussian blur parameter for image deblurring
IEEE Transactions on Signal Processing
A reduced Newton method for constrained linear least-squares problems
Journal of Computational and Applied Mathematics
IEEE Transactions on Image Processing
Cascadic multilevel methods for fast nonsymmetric blur- and noise-removal
Applied Numerical Mathematics
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
Adaptive Variational Method for Restoring Color Images with High Density Impulse Noise
International Journal of Computer Vision
Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction
IEEE Transactions on Image Processing
An MLP neural net with L1 and L2 regularizers for real conditions of deblurring
EURASIP Journal on Advances in Signal Processing
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
SIAM Journal on Imaging Sciences
Alternating Direction Method for Image Inpainting in Wavelet Domains
SIAM Journal on Imaging Sciences
Fast deconvolution with approximated PSF by RSTLS with antireflective boundary conditions
Journal of Computational and Applied Mathematics
Windowed Spectral Regularization of Inverse Problems
SIAM Journal on Scientific Computing
On decomposition-based block preconditioned iterative methods for half-quadratic image restoration
Journal of Computational and Applied Mathematics
Non-convex hybrid total variation for image denoising
Journal of Visual Communication and Image Representation
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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Blur removal is an important problem in signal and image processing. The blurring matrices obtained by using the zero boundary condition (corresponding to assuming dark background outside the scene) are Toeplitz matrices for one-dimensional problems and block-Toeplitz--Toeplitz-block matrices for two-dimensional cases. They are computationally intensive to invert especially in the block case. If the periodic boundary condition is used, the matrices become (block) circulant and can be diagonalized by discrete Fourier transform matrices. In this paper, we consider the use of the Neumann boundary condition (corresponding to a reflection of the original scene at the boundary). The resulting matrices are (block) Toeplitz-plus-Hankel matrices. We show that for symmetric blurring functions, these blurring matrices can always be diagonalized by discrete cosine transform matrices. Thus the cost of inversion is significantly lower than that of using the zero or periodic boundary conditions. We also show that the use of the Neumann boundary condition provides an easy way of estimating the regularization parameter when the generalized cross-validation is used. When the blurring function is nonsymmetric, we show that the optimal cosine transform preconditioner of the blurring matrix is equal to the blurring matrix generated by the symmetric part of the blurring function. Numerical results are given to illustrate the efficiency of using the Neumann boundary condition.