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Blind inverse problems with isolated spikes

Abstract : Assume that an unknown integral operator living in some known subspace is observed indirectly, by evaluating its action on a few Dirac masses at unknown locations. Is this information enough to recover the operator and the impulse responses locations stably? We study this question and answer positively under realistic technical assumptions. We illustrate the well-foundedness of this theory on two challenging optical imaging problems: blind super-resolution and deconvolution. This provides a simple, practical and theoretically grounded approach to solve these long resisting problems.
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Contributor : Pierre Weiss Connect in order to contact the contributor
Submitted on : Tuesday, November 2, 2021 - 10:25:40 PM
Last modification on : Sunday, November 27, 2022 - 6:12:55 AM


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Valentin Debarnot, Pierre Weiss. Blind inverse problems with isolated spikes. Information and Inference, 2022, ⟨10.1093/imaiai/iaac015⟩. ⟨hal-03272066v2⟩



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