Geodesic
A Convex Decomposition Formula for the Mumford-Shah Functional in Dimension One
Journal of convex analysis, Tome 25 (2018) no. 4, pp. 1197-1221
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We study the convex lift of Mumford-Shah type functionals in the space of rectifiable currents and we prove a convex decomposition formula in dimension one, for finite linear combinations of SBV graphs. We use this result to prove the equivalence between the minimum problems for the Mumford-Shah functional and the lifted one and, as a consequence, we obtain a weak existence result for calibrations in one dimension.
Classification : 49K99, 49Q20, 39B62
Mots-clés : Mumford-Shah functional, convex lift, rectifiable currents, calibrations 
@article{JCA_2018_25_4_JCA_2018_25_4_a7,
     author = {M. Carioni},
     title = {A {Convex} {Decomposition} {Formula} for the {Mumford-Shah} {Functional} in {Dimension} {One}},
     journal = {Journal of convex analysis},
     pages = {1197--1221},
     year = {2018},
     volume = {25},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2018_25_4_JCA_2018_25_4_a7/}
}
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M. Carioni. A Convex Decomposition Formula for the Mumford-Shah Functional in Dimension One. Journal of convex analysis, Tome 25 (2018) no. 4, pp. 1197-1221. http://geodesic.mathdoc.fr/item/JCA_2018_25_4_JCA_2018_25_4_a7/