Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourier Phase Retrieval: Uniqueness and Algorithms   The problem of recovering a signal from its phaseless Fourier transform
measurements, called Fourier phase retrieval, arises in many applications in
engineering and science. Fourier phase retrieval poses fundamental theoretical
and algorithmic challenges. In general, there is no unique mapping between a
one-dimensional signal and its Fourier magnitude and therefore the problem is
ill-posed. Additionally, while almost all multidimensional signals are uniquely
mapped to their Fourier magnitude, the performance of existing algorithms is
generally not well-understood. In this chapter we survey methods to guarantee
uniqueness in Fourier phase retrieval. We then present different algorithmic
approaches to retrieve the signal in practice. We conclude by outlining some of
the main open questions in this field.

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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
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The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: eess