The regularizing properties of the adjoint gradient method in ill-posed problems
USSR Computational Mathematics and Mathematical Physics
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multilevel grid method for history matching multi-dimensional multi-phase reservoir models
Applied Numerical Mathematics
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Modifying the QR-decomposition to constrained and weighted line linear last squares
SIAM Journal on Matrix Analysis and Applications
A Fast Algorithm for Deblurring Models with Neumann Boundary Conditions
SIAM Journal on Scientific Computing
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
ACM Transactions on Mathematical Software (TOMS)
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Breakdown-free GMRES for Singular Systems
SIAM Journal on Matrix Analysis and Applications
On the Regularizing Power of Multigrid-type Algorithms
SIAM Journal on Scientific Computing
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
Arnoldi-Tikhonov regularization methods
Journal of Computational and Applied Mathematics
Cascadic multilevel methods for ill-posed problems
Journal of Computational and Applied Mathematics
Cascadic Multiresolution Methods for Image Deblurring
SIAM Journal on Imaging Sciences
PDE-based deconvolution with forward-backward diffusivities and diffusion tensors
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
The staircasing effect in neighborhood filters and its solution
IEEE Transactions on Image Processing
A hybrid multilevel-active set method for large box-constrained linear discrete ill-posed problems
Calcolo: a quarterly on numerical analysis and theory of computation
Alternating Krylov subspace image restoration methods
Journal of Computational and Applied Mathematics
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Image deblurring is a discrete ill-posed problem. This paper discusses cascadic multilevel methods designed for the restoration of images that have been contaminated by nonsymmetric blur and noise. Prolongation is carried out by nonlinear edge-preserving and noise-reducing operators, while restrictions are determined by weighted local least-squares approximation. The restoration problem is on each level solved by an iterative method, with the number of iterations determined by the discrepancy principle. The performance of several iterative methods is compared. Computed examples demonstrate the effectiveness of the image restoration methods proposed. The discrepancy principle requires that an estimate of the norm of the noise in the contaminated image be available. We illustrate how such an estimate can be computed with the aid of the nonlinear Perona-Malik diffusion equation.