Graph regularization for color image processing
Computer Vision and Image Understanding
Total variation minimizing blind deconvolution with shock filter reference
Image and Vision Computing
Journal of Mathematical Imaging and Vision
Non-negatively constrained image deblurring with an inexact interior point method
Journal of Computational and Applied Mathematics
Some First-Order Algorithms for Total Variation Based Image Restoration
Journal of Mathematical Imaging and Vision
Optimal estimation of deterioration from diagnostic image sequence
IEEE Transactions on Signal Processing
Efficient minimization method for a generalized total variation functional
IEEE Transactions on Image Processing
Journal of Mathematical Imaging and Vision
An Augmented Lagrangian Method for TVg+L1-norm Minimization
Journal of Mathematical Imaging and Vision
Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction
IEEE Transactions on Image Processing
Variational method for super-resolution optical flow
Signal Processing
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
SIAM Journal on Imaging Sciences
A convex image segmentation: extending graph cuts and closed-form matting
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part III
SIAM Journal on Imaging Sciences
Optimal Allocation of a Futures Portfolio Utilizing Numerical Market Phase Detection
SIAM Journal on Financial Mathematics
Geophysical model enhancement technique based on blind deconvolution
Computers & Geosciences
Cascaded Evolutionary Estimator for Robot Localization
International Journal of Applied Evolutionary Computation
Advances in Computational Mathematics
Proximity algorithms for the L1/TV image denoising model
Advances in Computational Mathematics
Total variation regularization algorithms for images corrupted with different noise models: a review
Journal of Electrical and Computer Engineering
Hybrid regularization image deblurring in the presence of impulsive noise
Journal of Visual Communication and Image Representation
A linearly convergent first-order algorithm for total variation minimisation in image processing
International Journal of Bioinformatics Research and Applications
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Image restoration problems are often solved by finding the minimizer of a suitable objective function. Usually this function consists of a data-fitting term and a regularization term. For the least squares solution, both the data-fitting and the regularization terms are in the $\ell$2 norm. In this paper, we consider the least absolute deviation (LAD) solution and the least mixed norm (LMN) solution. For the LAD solution, both the data-fitting and the regularization terms are in the $\ell$1 norm. For the LMN solution, the regularization term is in the $\ell$1 norm but the data-fitting term is in the $\ell$2 norm. Since images often have nonnegative intensity values, the proposed algorithms provide the option of taking into account the nonnegativity constraint. The LMN and LAD solutions are formulated as the solution to a linear or quadratic programming problem which is solved by interior point methods. At each iteration of the interior point method, a structured linear system must be solved. The preconditioned conjugate gradient method with factorized sparse inverse preconditioners is employed to solve such structured inner systems. Experimental results are used to demonstrate the effectiveness of our approach. We also show the quality of the restored images, using the minimization of mixed $\ell$2-$\ell$1 and $\ell1$-$\ell$1 norms, is better than that using only the $\ell$2 norm.