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
Mathematical Programming: Series A and B
TV Based Image Restoration with Local Constraints
Journal of Scientific Computing
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
A TV Based Restoration Model with Local Constraints
Journal of Scientific Computing
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
Deblurring Poissonian images by split Bregman techniques
Journal of Visual Communication and Image Representation
On the total variation dictionary model
IEEE Transactions on Image Processing
Fast image recovery using variable splitting and constrained optimization
IEEE Transactions on Image Processing
Multiplicative Noise Removal with Spatially Varying Regularization Parameters
SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Operator Splittings, Bregman Methods and Frame Shrinkage in Image Processing
International Journal of Computer Vision
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
A Fast Algorithm for Euler's Elastica Model Using Augmented Lagrangian Method
SIAM Journal on Imaging Sciences
Augmented Lagrangian Method for Generalized TV-Stokes Model
Journal of Scientific Computing
Variational denoising of partly textured images by spatially varying constraints
IEEE Transactions on Image Processing
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In this paper, we propose two variational image denosing/deblurring models which combine tight frame regularization with two types of existing local constraints. Additive white Gaussian noise is assumed in the models. By Lagrangian multiplier method, the local constraints correspond to the fidelity term with spatial adaptive parameters. As the fidelity parameter is bigger in the image regions with textures than in the cartoon region, our models can recover more texture while denoising/deblurring. Fast numerical schemes are designed for the two models based on split Bregman (SB) technique and doubly augmented Lagrangian (DAL) method with acceleration. In the experiments, we show that the proposed models have better performance compared with the existing total variation based image restoration models with global or local constraints and the frame based model with global constraint.