Asymptotic Behaviour of Total Generalised Variation

Abstract. The recently introduced second order total generalised variation functional TGV2 β,α has been a successful regulariser for image processing purposes. Its definition involves two positive parameters α and β whose values determine the amount and the quality of the regularisation. In this paper we report on the behaviour of TGV2 β,α in the cases where the parameters α, β as well as their ratio β/α becomes very large or very small. Among others, we prove that for sufficiently symmetric two dimensional data and large ratio β/α, TGV2 β,α regularisation coincides with total variation (TV) regularisation.

• Type: Journal
• Year: 2015
• Where: SCALESPACE
• Authors: Konstantinos Papafitsoros, Tuomo Valkonen
• Keywords: Computer Vision, SCALESPACE 2015