The Interpolation Problem with TV(2) Regularization
Thomas Debarre

Meeting • 30 July 2019

Abstract
In this talk, we will study the 1D interpolation problem with TV(2) regularization using the tools of duality theory. We first present a complete description of the solution set. More precisely, we provide a characterization for unicity, and give the form of all the solutions when it is not, including the (possibly infinite) sparsest solutions. We then present an algorithm to solve the penalized interpolation problem, which produces one of the sparsest solutions of the problem given the data points and a regularization parameter.