Optimal design of sampling sets for least-squares signal recovery with the Frank-Wolfe algorithm

Abstract : We consider the sensors selection problem in a least-squares setting. The sensors selection is replaced by the relaxed problem of designing a sampling density minimizing the number of samples needed to ensure stability of the recovery, shown to be equivalent to the D-optimal design problem. We propose to use the Frank-Wolfe algorithm to solve this optimization problem, with low space and time computational complexity, linear with respect to the number of possible sensors positions. As the optimal densities are usually sparse, sampling points are drawn from the optimized density using resampling methods. The optimization problem and procedure can be easily modified to account for additional design constraints.
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https://hal.archives-ouvertes.fr/hal-01841900
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Submitted on : Tuesday, July 17, 2018 - 4:14:51 PM
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Gilles Chardon. Optimal design of sampling sets for least-squares signal recovery with the Frank-Wolfe algorithm. 2018. 〈hal-01841900〉

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