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Signal reconstruction from the magnitude of subspace components

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBACHOC, Christine
hal.structure.identifierFaculty of Mathematics [Vienna]
dc.contributor.authorEHLER, Martin
dc.date.accessioned2024-04-04T02:21:08Z
dc.date.available2024-04-04T02:21:08Z
dc.date.created2013
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189545
dc.description.abstractEnWe consider signal reconstruction from the norms of subspace components generalizing standard phase retrieval problems. In the deterministic setting, a closed reconstruction formula is derived when the subspaces satisfy certain cubature conditions, that require at least a quadratic number of subspaces. Moreover, we address reconstruction under the erasure of a subset of the norms; using the concepts of p-fusion frames and list decoding, we propose an algorithm that outputs a nite list of candidate signals, one of which is the correct one. In the random setting, we show that a set of subspaces chosen at random and of cardinality scaling linearly in the ambient dimension allows for exact reconstruction with high probability by solving the feasibility problem of a semide finite program
dc.language.isoen
dc.subjectsignal reconstruction
dc.subjectFusion frames
dc.title.enSignal reconstruction from the magnitude of subspace components
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Théorie de l'information et codage [math.IT]
dc.subject.halInformatique [cs]/Théorie de l'information [cs.IT]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-00880340
hal.version1
hal.audienceNon spécifiée
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00880340v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BACHOC,%20Christine&EHLER,%20Martin&rft.genre=preprint


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