Name: Andrea Borsic

Email: aborsic@brookes.ac.uk

CompanyName: Oxford Brookes University

Country: UK

Abstract: Overview of numerical methods for Total Variation regularisation

Andrea Borsic, Nickolas Polydorides, William Lionheart, Christopher N. McLeod

In this paper we present an overview of Total Variation regularisation techniques for
non--smooth inversion. The Total Variation functional is assuming an important role in the
regularisation of inverse problems belonging to many disciplines, thanks to its ability to
preserve discontinuities in the reconstructed profiles. Application of non-smooth
reconstruction techniques is important for medical and process imaging applications of EIT, as
they involve discontinuous profiles. Qualitative and quantitative benefits can be expected in
these fields. In the paper an outline of the properties of the TV (Total Variation) functional
will be given, to motivate its use as a regularisation penalty term and to understand the
numerical difficulties associated with it. The use of the TV functional leads in fact to the
formulation of the inverse problem as a minimisation of a non--differentiable function.
Application of traditional minimisation techniques (Steepest Descent Method, Newton Method)
has proven to be inefficient. Recent devolvements in non-smooth optimisation (Primal--Dual
Interior--Point Methods) have brought the means of dealing with the minimisation problem
efficiently. We will present numerical experiments of application of TV regularisation in EIT,
and comparisons of numerical methods.

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