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May 2015, 9(2): 511-550. doi: 10.3934/ipi.2015.9.511
A study of the one dimensional total generalised variation regularisation problem
Konstantinos Papafitsoros 1, and Kristian Bredies 2,
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, CB3 0WA, Cambridge, United Kingdom
Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, A-8010, Graz, Austria
Received October 2013 Revised October 2014 Published March 2015
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: total generalised variation, Higher order regularisation, exact solutions, staircasing., denoising.
Mathematics Subject Classification: Primary: 26B30, 49Q20, 65J2.
Citation: Konstantinos Papafitsoros, Kristian Bredies. A study of the one dimensional total generalised variation regularisation problem. Inverse Problems & Imaging, 2015, 9 (2) : 511-550. doi: 10.3934/ipi.2015.9.511
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Konstantinos Papafitsoros Kristian Bredies