Compressed sensing with unknown sensor permutation

Valentin Emiya 1 Antoine Bonnefoy 1 Laurent Daudet 2 Rémi Gribonval 3
1 QARMA - éQuipe AppRentissage et MultimediA [Marseille]
LIF - Laboratoire d'informatique Fondamentale de Marseille
3 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : Compressed sensing is the ability to retrieve a sparse vector from a set of linear measurements. The task gets more difficult when the sensing process is not perfectly known. We address such a problem in the case where the sensors have been permuted, i.e., the order of the measurements is unknown. We propose a branch-and-bound algorithm that converges to the solution. The experimental study shows that our approach always retrieves the unknown permutation, while a simple convex relaxation strategy almost always fails. In terms of its time complexity, we show that the proposed algorithm converges quickly with respect to the combinatorial nature of the problem.
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Valentin Emiya, Antoine Bonnefoy, Laurent Daudet, Rémi Gribonval. Compressed sensing with unknown sensor permutation. ICASSP - IEEE International Conference on Acoustics Speech and Signal Processing, May 2014, Florence, Italy. ⟨10.1109/ICASSP.2014.6853755⟩. ⟨hal-00881407v2⟩

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