BACHOC, Christine; EHLER, Martin

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BACHOC, Christine
Institut de Mathématiques de Bordeaux [IMB]

EHLER, Martin
Faculty of Mathematics [Vienna]

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Document de travail - Pré-publication

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We 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< Leer menos

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signal reconstruction

Fusion frames

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Signal reconstruction from the magnitude of subspace components

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