Mathematics Colloquia and Seminars

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Phase retrieval is one of the classic inverse problems arising from X-ray crystallography. In the far-field limit diffraction approximates a Fourier transform however it is technologically challenging to measure the phase of an X-ray. We study null-initialization, a particular spectral method for recovering phase. In particular, we aim to answer questions about the robustness of null-initialization, especially a low signal-to-noise regime where one can only record energy at particular thresholds or must count individual photons. We will explore a connection to the spiked Wishart model in random matrix theory to give an information-theoretic prediction for when an estimate through null-initialization will have non-trivial correlation with the signal. Along the way we encounter some beautiful relationships between the chi-square, poisson, geometric and binomial distributions.

Free pizzas as always:)