Nov 21 – 22, 2023
Institut Henri Poincaré
Europe/Paris timezone

Towards optimal sensor placement for inverse problems in spaces of measures

Nov 22, 2023, 11:10 AM
Amphithéâtre Hermite (Institut Henri Poincaré)

Amphithéâtre Hermite

Institut Henri Poincaré


Daniel Walter (Humboldt Universität zu Berlin)


In this talk, we study the identification of a linear combination of point sources from a finite number of measurements contaminated by random noise. It relies on two main ingredients, first, a convex but non-smooth Tikhonov point estimator over the space of Radon measures and, second, a suitable
mean-squared error based on its Hellinger-Kantorovich distance to the ground truth. Assuming standard non-degenerate source conditions as well as applying careful linearization arguments, a computable upper bound on the latter is derived. On the one hand, this allows to derive asymptotic convergence results for the mean-squared error of the estimator in the small small variance case.
On the other, it paves the way for applying optimal sensor placement approaches to sparse inverse problems.

Primary author

Daniel Walter (Humboldt Universität zu Berlin)

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