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Total variation based Lavrentiev regularisation

Banff International Research Station for Mathematical Innovation and Discovery

In this talk we will discuss a non-linear variant of Lavrentiev regularisation, where the sub-differential of the total variation replaces the identity operator as regularisation term. The advantage of this approach over Tikhonov based total variation regularisation is that it avoids the evaluation of the adjoint operator on the data. As a consequence, it can be used, for instance, for the solution of Volterra integral equations of the first kind, where the adjoint would require an integration forward in time, without the need of accessing future data points. We will discuss first the theoretical properties of this method, and then propose a taut-string based numerical method for the solution of one-dimensional problems.

Mathematics; Functional analysis; Calculus of variations and optimal control; optimization; Numerical analysis

video/mp4

Author affiliation: Norwegian University of Science and Technology

2019-12-23

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72916

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/