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Article Dans Une Revue SIAM Journal on Imaging Sciences Année : 2024

Polarimetric Fourier phase retrieval

Résumé

This work introduces polarimetric Fourier phase retrieval (PPR), a physically inspired model to leverage polarization of light information in Fourier phase retrieval problems. We provide a complete characterization of its uniqueness properties by unraveling equivalencies with two related problems, namely, bivariate phase retrieval and a polynomial autocorrelation factorization problem. In particular, we show that the problem admits a unique solution, which can be formulated as a greatest common divisor (GCD) of measurement polynomials. As a result, we propose algebraic solutions for PPR based on approximate GCD computations using the null-space properties of Sylvester matrices. Alternatively, existing iterative algorithms for phase retrieval, semidefinite positive relaxation and Wirtinger flow, are carefully adapted to solve the PPR problem. Finally, a set of numerical experiments permits a detailed assessment of the numerical behavior and relative performances of each proposed reconstruction strategy. They further demonstrate the fruitful combination of algebraic and iterative approaches toward a scalable, computationally efficient, and robust to noise reconstruction strategy for PPR.
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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)

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Julien Flamant, Konstantin Usevich, Marianne Clausel, David Brie. Polarimetric Fourier phase retrieval. SIAM Journal on Imaging Sciences, 2024, pp.632-671. ⟨10.1137/23M1570971⟩. ⟨hal-03613352v4⟩
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