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
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Dual Norms and Image Decomposition Models
International Journal of Computer Vision
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
A Predual Proximal Point Algorithm Solving a Non Negative Basis Pursuit Denoising Model
International Journal of Computer Vision
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
On the Uniqueness of Nonnegative Sparse Solutions to Underdetermined Systems of Equations
IEEE Transactions on Information Theory
Minimizing the total variation under a general convex constraint for image restoration
IEEE Transactions on Image Processing
Iterative Regularization and Nonlinear Inverse Scale Space Applied to Wavelet-Based Denoising
IEEE Transactions on Image Processing
Deconvolving Poissonian images by a novel hybrid variational model
Journal of Visual Communication and Image Representation
Image Restoration via Tight Frame Regularization and Local Constraints
Journal of Scientific Computing
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The goal of this paper is to provide a theoretical study of a total variation (TV) dictionary model. Based on the properties of convex analysis and bounded variation functions, the existence of solutions of the TV dictionary model is proved. We then show that the dual form of the model can be given by the minimization of the sum of the l1-norm of the dual solution and the Bregman distance between the curvature of the primal solution and the subdifferential of TV norm of the dual solution. This theoretical result suggests that the dictionary must represent sparsely the curvatures of solution image in order to obtain a better denoising performance.