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
The nature of statistical learning theory
The nature of statistical learning theory
Regularization, Scale-Space, and Edge Detection Filters
Journal of Mathematical Imaging and Vision
An equivalence between sparse approximation and support vector machines
Neural Computation
Relations Between Regularization and Diffusion Filtering
Journal of Mathematical Imaging and Vision
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
High-Order Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Tube Methods for BV Regularization
Journal of Mathematical Imaging and Vision
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
SIAM Journal on Numerical Analysis
Taut-String Algorithm and Regularization Programs with G-Norm Data Fit
Journal of Mathematical Imaging and Vision
Nonlinear evolution equations as fast and exact solvers of estimation problems
IEEE Transactions on Signal Processing
Fourth-order partial differential equations for noise removal
IEEE Transactions on Image Processing
Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection
International Journal of Computer Vision
Splines in Higher Order TV Regularization
International Journal of Computer Vision
The Equivalence of the Taut String Algorithm and BV-Regularization
Journal of Mathematical Imaging and Vision
Properties of Higher Order Nonlinear Diffusion Filtering
Journal of Mathematical Imaging and Vision
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We study the connection between higher order total variation (TV) regularization and support vector regression (SVR) with spline kernels in a one-dimensional discrete setting. We prove that the contact problem arising in the tube formulation of the TV minimization problem is equivalent to the SVR problem. Since the SVR problem can be solved by standard quadratic programming methods this provides us with an algorithm for the solution of the contact problem even for higher order derivatives. Our numerical experiments illustrate the approach for various orders of derivatives and show its close relation to corresponding nonlinear diffusion and diffusion–reaction equations.