Properties of exact solutions to the problem of regularization of the total variation of one-variable functions

Abstract

In this study, an exact solution to the variational problem of minimization of a functional consisting of an accuracy term and a regularization term is considered. The regularization term is the total variation of a one-variable function. The variational problem under consideration is widely used in the theory of image and signal restoration. As the weighting factor of total variation increases, the exact solution to the variational problem becomes a more smoothed function. A method for calculating exact solutions and the properties of these solutions are described.