2021
DOI: 10.48550/arxiv.2109.14522
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Lipschitz Analysis of Generalized Phase Retrievable Matrix Frames

Abstract: The classical phase retrieval problem arises in contexts ranging from speech recognition to x-ray crystallography and quantum state tomography. The generalization to matrix frames is natural in the sense that it corresponds to quantum tomography of impure states. We provide computable global stability bounds for the quasi-linear analysis map β and a path forward for understanding related problems in terms of the differential geometry of key spaces. In particular, we manifest a Whitney stratification of the pos… Show more

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“…Upper and lower Lipschitz bounds are used to quantify the stability of a mapping between metric spaces, but it is generally difficult to estimate such bounds; see [9,7,17,45,5] for examples from phase retrieval and [79,19,18,6] for other examples. In this subsection, we prove the following:…”
Section: Stability Of Max Filtering 41 Bilipschitz Max Filter Banksmentioning
confidence: 99%
“…Upper and lower Lipschitz bounds are used to quantify the stability of a mapping between metric spaces, but it is generally difficult to estimate such bounds; see [9,7,17,45,5] for examples from phase retrieval and [79,19,18,6] for other examples. In this subsection, we prove the following:…”
Section: Stability Of Max Filtering 41 Bilipschitz Max Filter Banksmentioning
confidence: 99%