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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.<\/jats:p>","DOI":"10.1137\/23m1570971","type":"journal-article","created":{"date-parts":[[2024,3,11]],"date-time":"2024-03-11T04:24:53Z","timestamp":1710131093000},"page":"632-671","source":"Crossref","is-referenced-by-count":1,"title":["Polarimetric Fourier Phase Retrieval"],"prefix":"10.1137","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9994-173X","authenticated-orcid":true,"given":"Julien","family":"Flamant","sequence":"first","affiliation":[{"name":"Corresponding author. 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