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

Farah Cherfaoui; Valentin Emiya; Liva Ralaivola; Sandrine Anthoine

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

Farah Cherfaoui ¹ Valentin Emiya ¹ Liva Ralaivola ¹ Sandrine Anthoine ²

1 QARMA - éQuipe d'AppRentissage de MArseille

LIS - Laboratoire d'Informatique et Systèmes

2 I2M - Institut de Mathématiques de Marseille

Abstract : 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 signal is sparse enough with respect to the coherence of the dictionary, 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 under this same condition, there exists an iteration beyond which the algorithm converges exponentially.

Keywords : recovery properties Frank-Wolfe algorithm sparse representation exponential convergence

Document type :

Journal articles

Domain :

Computer Science [cs] / Signal and Image Processing

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https://hal.archives-ouvertes.fr/hal-01919761
Contributor : Farah Cherfaoui <>
Submitted on : Friday, May 17, 2019 - 5:12:40 PM
Last modification on : Tuesday, May 28, 2019 - 1:29:38 AM

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

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