Density matrix reconstructions in ultrafast transmission electron microscopy: 
Uniqueness, stability, and convergence rates

Shi, C.; Ropers, Claus; Hohage, T.

doi:10.1088/1361-6420/ab539a

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Density matrix reconstructions in ultrafast transmission electron microscopy: Uniqueness, stability, and convergence rates

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Ropers, Claus
Department of Ultrafast Dynamics, MPI for Biophysical Chemistry, Max Planck Society;

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Shi, C., Ropers, C., & Hohage, T. (2020). Density matrix reconstructions in ultrafast transmission electron microscopy: Uniqueness, stability, and convergence rates. Inverse Problems, 36(2): 025005. doi:10.1088/1361-6420/ab539a.

Cite as: https://hdl.handle.net/21.11116/0000-000B-57A6-8

Abstract

In the recent paper Priebe et al (2017 Nat. Photon. 11 793–7) the first experimental determination of the density matrix of a free electron beam has been reported. The employed method leads to a linear inverse problem with a positive semidefinite operator as unknown. The purpose of this paper is to complement the experimental and algorithmic results in the work mentioned above by a mathematical analysis of the inverse problem concerning uniqueness, stability, and rates of convergence under different types of a priori information.