Inverse Problems and Imaging (IPI)

A study of the one dimensional total generalised variation regularisation problem

Pages: 511 - 550, Volume 9, Issue 2, May 2015      doi:10.3934/ipi.2015.9.511

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Konstantinos Papafitsoros - Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, CB3 0WA, Cambridge, United Kingdom (email)
Kristian Bredies - Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, A-8010, Graz, Austria (email)

Abstract: In this paper we study the one dimensional second order total generalised variation regularisation (TGV) problem with $L^{2}$ data fitting term. We examine the properties of this model and we calculate exact solutions using simple piecewise affine functions as data terms. We investigate how these solutions behave with respect to the TGV parameters and we verify our results using numerical experiments.

Keywords:  Higher order regularisation, total generalised variation, denoising, exact solutions, staircasing.
Mathematics Subject Classification:  Primary: 26B30, 49Q20, 65J20.

Received: October 2013;      Revised: October 2014;      Available Online: March 2015.