© 2015 American Institute of Mathematical Sciences. In this paper we study the one dimensional second order total generalised variation regularisation (TGV) problem with L2 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.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1007-43
Acknowledgements: The first author was supported by UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/H023348/1 for the University of Cambridge Centre for Doctoral Training, the Cambridge Centre for Analysis, the financial support provided by the EPSRC first grant Nr. EP/J009539/1 ''Sparse & Higher-order Image Restoration" and the Award No. KUK-I1007-43, made by King Abdullah University of Science and Technology (KAUST). The second author is supported by the Austrian Science Fund (FWF) under grant SFB32 (SFB ''Mathematical Optimization and Applications in the Biomedical Sciences").
This publication acknowledges KAUST support, but has no KAUST affiliated authors.