Polarimetric Fourier phase retrieval - CRAN-BioSiS Accéder directement au contenu
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.
Fichier principal
Vignette du fichier
M157097.pdf (5.49 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

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

Citer

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⟩
175 Consultations
118 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More