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Limiting aspects of non-convex TVϕ models
Hintermüller, Micha...

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Limiting aspects of non-convex TVϕ models by Hintermüller, Michael ( Author )
Lemonjar Open Access
N.A
23-12-2014
Recently, non-convex regularisation 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 still TVϕ(u)=∞ for u not piecewise constant. If, on the other hand, TVϕ is defined analogously via continuously differentiable functions, then TVϕ≡0, (!). We study a way to remedy the models through additional multiscale regularisation and area strict convergence, provided that the energy ϕ(t)=tq is linearised for high values. The fact, that this kind of energies actually better matches reality and improves reconstructions, is demonstrated by statistics and numerical experiments.
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English
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MYR 0.01
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doi:10.1137/141001457
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