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Pré-Publication, Document De Travail Année : 2022

Polarimetric phase retrieval : uniqueness and algorithms

Marianne Clausel
David Brie

Résumé

This work introduces a novel Fourier phase retrieval model, called polarimetric phase retrieval that enables a systematic use of polarization information in Fourier phase retrieval problems. We provide a thorough characterization of uniqueness properties of this new model by unraveling equivalencies with a peculiar polynomial factorization problem. We introduce two different but complementary categories of reconstruction methods. The first one is algebraic and relies on the use of approximate greatest common divisor computations using Sylvester matrices. The second one carefully adapts existing algorithms for Fourier phase retrieval, namely semidefinite positive relaxation and Wirtinger-Flow, to solve the polarimetric phase retrieval problem. Finally, a set of numerical experiments permits a thorough assessment of the numerical behavior and relative performances of each proposed reconstruction strategy. We further highlight a reconstruction strategy that combines both approaches for scalable, computationally efficient and asymptotically MSE optimal performance.
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Dates et versions

hal-03613352 , version 1 (18-03-2022)
hal-03613352 , version 2 (28-06-2022)
hal-03613352 , version 3 (07-04-2023)
hal-03613352 , version 4 (11-03-2024)

Identifiants

  • HAL Id : hal-03613352 , version 2

Citer

Julien Flamant, Konstantin Usevich, Marianne Clausel, David Brie. Polarimetric phase retrieval : uniqueness and algorithms. 2022. ⟨hal-03613352v2⟩
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