Relations Between Higher Order TV Regularization and Support Vector Regression

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.