Show simple item record

2015-11-10Zeitschriftenartikel DOI: 10.18452/13696
Limiting Aspects of Nonconvex TV^phi Models
dc.contributor.authorHintermüller, M.
dc.contributor.authorValkonen, T.
dc.contributor.authorWu, T.
dc.date.accessioned2017-06-17T16:15:51Z
dc.date.available2017-06-17T16:15:51Z
dc.date.created2017-05-08
dc.date.issued2015-11-10
dc.identifier.other10.1137/141001457
dc.identifier.urihttp://edoc.hu-berlin.de/18452/14348
dc.description.abstractRecently, nonconvex regularization models have been introduced in order to provide a better prior for gradient distributions in real images. They are based on using concave energies φ in the total variation–type functional TVφ (u) := φ(|∇u(x)|) dx. In this paper, it is demonstrated that for typical choices of φ, functionals of this type pose several difficulties when extended to the entire space of functions of bounded variation, BV(Ω). In particular, if φ(t) = tq for q ∈ (0, 1), and TVφ is defined directly for piecewise constant functions and extended via weak* lower semicontinuous envelopes to BV(Ω), then it still holds that TVφ (u) = ∞ for u not piecewise constant. If, on the other hand, TVφ is defined analogously via continuously differentiable functions, then TV φ ≡ 0 (!). We study a way to remedy the models through additional multiscale regularization and area strict convergence, provided that the energy φ(t) = tq is linearized for high values. The fact that such energies actually better match reality and improve reconstructions is demonstrated by statistics and numerical experiments.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät
dc.subjecttotal variationeng
dc.subjectnonconvexeng
dc.subjectarea-strict convergenceeng
dc.subjectmultiscale analysiseng
dc.subject.ddc510 Mathematik
dc.titleLimiting Aspects of Nonconvex TV^phi Models
dc.typearticle
dc.identifier.urnurn:nbn:de:kobv:11-100246486
dc.identifier.doihttp://dx.doi.org/10.18452/13696
local.edoc.container-titleSIAM Journal on Imaging Sciences
local.edoc.anmerkung© 2015, Society for Industrial and Applied Mathematics
local.edoc.type-nameZeitschriftenartikel
local.edoc.institutionMathematisch-Naturwissenschaftliche Fakultät
local.edoc.container-typeperiodical
local.edoc.container-type-nameZeitschrift
local.edoc.container-publisher-nameSociety for Industrial and Applied Mathematics
local.edoc.container-volume8
local.edoc.container-issue4
local.edoc.container-year2015
local.edoc.container-firstpage2581
local.edoc.container-lastpage2621
dc.description.versionPeer Reviewed

Show simple item record