TY - ELEC
AU - Markus Grasmair
PY - 2019
TI - Total variation based Lavrentiev regularisation
LA - eng
M3 - Moving Image
AB - 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.
N2 - 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.
UR - https://open.library.ubc.ca/collections/48630/items/1.0387279
ER - End of Reference