Signal reconstruction from the magnitude of subspace components

Christine Bachoc (1) , Martin Ehler (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 Faculty of Mathematics [Vienna]

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

Mots clés: signal reconstruction; Fusion frames

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Christine Bachoc, Martin Ehler. Signal reconstruction from the magnitude of subspace components. 2013. ⟨hal-00880340⟩