A relaxation result for an inhomogeneous functional preserving point-like and curve-like singularities in image processing

Gilles Aubert 1 Daniele Graziani 2
2 MORPHEME - Morphologie et Images
CRISAM - Inria Sophia Antipolis - Méditerranée , IBV - Institut de Biologie Valrose : U1091, Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : In the present paper we address a relaxation theorem for a new integral functional of the calculus of variations de ned on the space of functions in W1;p loc whose gradient is an Lp-vector eld with distributional divergence given by a Radon measure. The result holds for integrand of type f(x; u) without any coerciveness condition, with respect to the second variable, and C1-continuity assumptions with respect to the spatial variable x.
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https://hal.inria.fr/inria-00536206
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Submitted on : Wednesday, September 19, 2012 - 8:54:47 AM
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Gilles Aubert, Daniele Graziani. A relaxation result for an inhomogeneous functional preserving point-like and curve-like singularities in image processing. 2012. ⟨inria-00536206v3⟩

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