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Geometry of Optimal Decomposition for the Couple (2, X) on Rn
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-8188-7672
##### Abstract [en]

We investigate the geometry of optimal decomposition for the L– functional

$L_{2,1}(t, x; \ell{^2}, X) = \; \inf_{ x =x_0+x_1} \; \left(\frac{1}{2}\left\|x_{0}\right\|^{2}_{\ell^{2}}+t\left\|x_{1}\right\|_{X}\right)\;,$

where space ℓ2 is defined by the standard Euclidean norm $\left\|.\right\|_{2}$ and where X is a Banach space on Rn and t is a given positive parameter. Our proof is based on some geometrical considerations and Yves Meyer’s duality approach which was considered for the couple (L2, BV) in connection with the famous in image processing ROF denoising model. Our goal is also to investigate possibility to extend Meyer’s approach to more general couples than (L2, BV) .

##### Series
LiTH-MAT-R, ISSN 0348-2960 ; 6
Mathematics
##### Identifiers
ISRN: LiTH-MAT-R--2013/06--SEOAI: oai:DiVA.org:liu-94145DiVA: diva2:629624
Available from: 2013-06-17 Created: 2013-06-17 Last updated: 2014-05-27

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Geometry of Optimal Decomposition forthe Couple (ℓ2, X) on Rn(1206 kB)125 downloads
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Niyobuhungiro, Japhet
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