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
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing
Journal of Scientific Computing
Image Denoising and Decomposition with Total Variation Minimization and Oscillatory Functions
Journal of Mathematical Imaging and Vision
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
Image decomposition application to SAR images
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
IEEE Transactions on Image Processing
Minimizing the total variation under a general convex constraint for image restoration
IEEE Transactions on Image Processing
(Φ,Φ*) Image Decomposition Models and Minimization Algorithms
Journal of Mathematical Imaging and Vision
Fast cartoon + texture image filters
IEEE Transactions on Image Processing
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We propose a new model for image decomposition which separates an image into a cartoon, consisting only of geometric objects, and an oscillatory component, consisting of textures and noise. The model is given in a variational formulation with adaptive regularization norms for both the cartoon and texture part. The energy for the cartoon interpolates between total variation regularization and isotropic smoothing, while the energy for the textures interpolates between Meyer's G norm and the H−−1 norm. These energies are dual in the sense of the Legendre-Fenchel transform and their adaptive behavior preserves key features such as object boundaries and textures while avoiding staircasing in what should be smooth regions. Existence and uniqueness of a solution is established and experimental results demonstrate the effectiveness of the model for both grayscale and color image decomposition.