A study of the one dimensional  total generalised variation regularisation problem

Konstantinos Papafitsoros; Kristian Bredies

doi:10.3934/ipi.2015.9.511

Article Contents

2015, Volume 9, Issue 2: 511-550. Doi: 10.3934/ipi.2015.9.511

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A study of the one dimensional total generalised variation regularisation problem

Konstantinos Papafitsoros^1, and
Kristian Bredies^2,

1.
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, CB3 0WA, Cambridge
2.
Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, A-8010, Graz

Received: September 30, 2013

Revised: September 30, 2014

Published: April 2015

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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.

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Mathematics Subject Classification: Primary: 26B30, 49Q20, 65J20.

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