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• W3108183159 abstract "In this paper, we develop a novel framework to guide the design of initial estimates for phase retrieval given measurements realized from an arbitrary forward model. Particularly, we propose a general formalism for spectral initialization as an approximate Bregman loss minimization procedure in the range of the lifted forward model, such that a search over rank-1, positive semidefinite matrices is tractable by the synthesis of a quadratic form using elementwise processing of the intensity-only measurements. Via the Bregman loss approach we transcend the Euclidean sense alignment based similarity measure between phaseless measurements that is inherent in the state-of-the art techniques in the literature, in favor of information theory inspired divergence metrics over the positive reals. We derive spectral methods that perform approximate minimization of Kullback--Leibler and Itakura--Saito divergences over phaseless measurements by using elementwise sample processing functions which are designed under a minimal distortion principle. Our formulation relates and extends existing results on model dependent design of optimal sample processing functions in the literature to a model independent sense of metric-based optimality. Numerical simulations confirm the effectiveness of our approach in imaging problems using synthetic and real data sets." @default.
• W3108183159 created "2020-12-07" @default.
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• W3108183159 date "2022-04-14" @default.
• W3108183159 modified "2023-09-27" @default.
• W3108183159 title "A Spectral Estimation Framework for Phase Retrieval via Bregman Divergence Minimization" @default.
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• W3108183159 doi "https://doi.org/10.1137/20m1388061" @default.
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