About: Variational Coupling Revisited: Simpler Models, Theoretical Connections, and Novel Applications

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Attributes	Values
type	Academic Article research paper schema:ScholarlyArticle
isDefinedBy	Covid-on-the-Web dataset
has title	Variational Coupling Revisited: Simpler Models, Theoretical Connections, and Novel Applications
Creator	Weickert, Joachim Wewior, Aaron
Source	ArXiv
abstract	Variational models with coupling terms are becoming increasingly popular in image analysis. They involve auxiliary variables, such that their energy minimisation splits into multiple fractional steps that can be solved easier and more efficiently. In our paper we show that coupling models offer a number of interesting properties that go far beyond their obvious numerical benefits. We demonstrate that discontinuity-preserving denoising can be achieved even with quadratic data and smoothness terms, provided that the coupling term involves the $L^1$ norm. We show that such an $L^1$ coupling term provides additional information as a powerful edge detector that has remained unexplored so far. While coupling models in the literature approximate higher order regularisation, we argue that already first order coupling models can be useful. As a specific example, we present a first order coupling model that outperforms classical TV regularisation. It also establishes a theoretical connection between TV regularisation and the Mumford-Shah segmentation approach. Unlike other Mumford-Shah algorithms, it is a strictly convex approximation, for which we can guarantee convergence of a split Bregman algorithm.
has issue date	2019-12-12(xsd:dateTime)
has license	arxiv
sha1sum (hex)	9b17f8546c3e05d208dd9170c861a534f2eb4a9b
resource representing a document's title	Variational Coupling Revisited: Simpler Models, Theoretical Connections, and Novel Applications
resource representing a document's body	covid:9b17f8546c3e05d208dd9170c861a534f2eb4a9b#body_text
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