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
Convex analysis and variational problems
Convex analysis and variational problems
An Iterative Method with Variable Relaxation Parameters for Saddle-Point Problems
SIAM Journal on Matrix Analysis and Applications
A Variational Approach to Remove Outliers and Impulse Noise
Journal of Mathematical Imaging and Vision
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Efficient Minimization Methods of Mixed l2-l1 and l1-l1 Norms for Image Restoration
SIAM Journal on Scientific Computing
Handbook of Image and Video Processing (Communications, Networking and Multimedia)
Handbook of Image and Video Processing (Communications, Networking and Multimedia)
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Nonlinear Optimization
Lagrange Multiplier Approach to Variational Problems and Applications
Lagrange Multiplier Approach to Variational Problems and Applications
A Fast $\ell$1-TV Algorithm for Image Restoration
SIAM Journal on Scientific Computing
An Efficient TVL1 Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise
SIAM Journal on Scientific Computing
Efficient minimization method for a generalized total variation functional
IEEE Transactions on Image Processing
An Efficient Primal-Dual Method for $L^1$TV Image Restoration
SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
A property of the minimum vectors of a regularizing functionaldefined by means of the absolute norm
IEEE Transactions on Signal Processing
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A novel splitting method is presented for the $\ell^1$-$TV$ restoration of degraded images subject to impulsive noise. The functional is split into an $\ell^2$-$TV$ denoising part and an $\ell^1$-$\ell^2$ deblurring part. The dual problem of the relaxed functional is smooth with convex constraints and can be solved efficiently by applying an Arrow-Hurwicz-type algorithm to the augmented Lagrangian formulation. The regularization parameter is chosen automatically based on a balancing principle. The accuracy, the fast convergence, and the robustness of the algorithm and the use of the parameter choice rule are illustrated on some benchmark images and compared with an existing method.