Iterative methods for total variation denoising
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
On the Convergence of the Lagged Diffusivity Fixed Point Method in Total Variation Image Restoration
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
A Variational Approach to Remove Outliers and Impulse Noise
Journal of Mathematical Imaging and Vision
An interior-point method for large constrained discrete ill-posed problems
Journal of Computational and Applied Mathematics
Efficient minimization method for a generalized total variation functional
IEEE Transactions on Image Processing
Adaptive total variation denoising based on difference curvature
Image and Vision Computing
Updating preconditioners for nonlinear deblurring and denoising image restoration
Applied Numerical Mathematics
Tikhonov regularization based on generalized Krylov subspace methods
Applied Numerical Mathematics
The Equivalence of Half-Quadratic Minimization and the Gradient Linearization Iteration
IEEE Transactions on Image Processing
An Expanded Theoretical Treatment of Iteration-Dependent Majorize-Minimize Algorithms
IEEE Transactions on Image Processing
Nonlinear image recovery with half-quadratic regularization
IEEE Transactions on Image Processing
Adaptive regularization-based space-time super-resolution reconstruction
Image Communication
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We propose an adaptive norm strategy designed for the re-storation of images contaminated by blur and noise. Standard Tikhonov regularization can give good results with Gaussian noise and smooth images, but can over-smooth the output. On the other hand, L1 -TV (Total Variation) regularization has superior performance with some non-Gaussian noise and controls both the size of jumps and the geometry of the object boundaries in the image but smooth parts of the recovered images can be blocky. According to a coherence map of the image which is obtained by a threshold structure tensor, and can detect smooth regions and edges in the image, we apply L2 -norm or L1 -norm regularization to different parts of the image. The solution of the resulting minimization problem is obtained by a fast algorithm based on the half-quadratic technique recently proposed in [2] for L1 -TV regularization. Some numerical results show the effectiveness of our adaptive norm image restoration strategy.