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Pré-Publication, Document De Travail Année : 2018

Recovery and convergence rate of the Frank-Wolfe Algorithm for the m-EXACT-SPARSE Problem

Farah Cherfaoui
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Valentin Emiya
Liva Ralaivola

Résumé

We study the properties of the Frank-Wolfe algorithm to solve the m-EXACT-SPARSE reconstruction problem, where a signal y must be expressed as a sparse linear combination of a predefined set of atoms, called dictionary. We prove that when the dictionary is quasi-incoherent, then the iterative process implemented by the Frank-Wolfe algorithm only recruits atoms from the support of the signal, that is the smallest set of atoms from the dictionary that allows for a perfect reconstruction of y. We also prove that when the dictionary is quasi-incoherent, there exists an iteration beyond which the algorithm converges exponentially.
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Dates et versions

hal-01919761 , version 1 (12-11-2018)
hal-01919761 , version 2 (17-05-2019)

Identifiants

  • HAL Id : hal-01919761 , version 1

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Farah Cherfaoui, Valentin Emiya, Liva Ralaivola, Sandrine Anthoine. Recovery and convergence rate of the Frank-Wolfe Algorithm for the m-EXACT-SPARSE Problem. 2018. ⟨hal-01919761v1⟩
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