Discrete cosine transform: algorithms, advantages, applications
Discrete cosine transform: algorithms, advantages, applications
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
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Efficient projections onto the l1-ball for learning in high dimensions
Proceedings of the 25th international conference on Machine learning
Probing the Pareto Frontier for Basis Pursuit Solutions
SIAM Journal on Scientific Computing
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
Removing Multiplicative Noise by Douglas-Rachford Splitting Methods
Journal of Mathematical Imaging and Vision
IEEE Transactions on Image Processing
Deblurring Poissonian images by split Bregman techniques
Journal of Visual Communication and Image Representation
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
SIAM Journal on Scientific Computing
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
Convex Analysis and Monotone Operator Theory in Hilbert Spaces
Convex Analysis and Monotone Operator Theory in Hilbert Spaces
On vector and matrix median computation
Journal of Computational and Applied Mathematics
Foundations and Trends® in Machine Learning
Just relax: convex programming methods for identifying sparse signals in noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Image Processing
Total Variation Projection With First Order Schemes
IEEE Transactions on Image Processing
Hessian-Based Norm Regularization for Image Restoration With Biomedical Applications
IEEE Transactions on Image Processing
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Recently convex optimization models were successfully applied for solving various problems in image analysis and restoration. In this paper, we are interested in relations between convex constrained optimization problems of the form $\operatorname{argmin}\{ \varPhi(x) \mbox{ subject to } \varPsi(x) \le\tau\}$ and their penalized counterparts $\operatorname{argmin}\{\varPhi(x) + \lambda\varPsi(x)\}$ . We recall general results on the topic by the help of an epigraphical projection. Then we deal with the special setting 驴:=驴L驴驴 with L驴驴 m,n and 驴:=驴(H驴), where H驴驴 n,n and 驴:驴 n 驴驴驴{+驴} meet certain requirements which are often fulfilled in image processing models. In this case we prove by incorporating the dual problems that there exists a bijective function such that the solutions of the constrained problem coincide with those of the penalized problem if and only if 驴 and 驴 are in the graph of this function. We illustrate the relation between 驴 and 驴 for various problems arising in image processing. In particular, we point out the relation to the Pareto frontier for joint sparsity problems. We demonstrate the performance of the constrained model in restoration tasks of images corrupted by Poisson noise with the I-divergence as data fitting term 驴 and in inpainting models with the constrained nuclear norm. Such models can be useful if we have a priori knowledge on the image rather than on the noise level.