Blind inverse problems with isolated spikes

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 positiv...

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Bibliographic Details
Published inInformation and inference Vol. 12; no. 1; pp. 26 - 71
Main Authors Debarnot, Valentin, Weiss, Pierre
Format Journal Article
LanguageEnglish
Published Oxford University Press (OUP) 02.02.2023
Subjects
Computer Science
Information Theory
Mathematics
Optimization and Control
Signal and Image Processing
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Summary: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.
ISSN:2049-8764
2049-8772
DOI:10.1093/imaiai/iaac015