Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blind Phaseless Short-Time Fourier Transform Recovery   The problem of recovering a pair of signals from their blind phaseless
short-time Fourier transform measurements arises in several important phase
retrieval applications, including ptychography and ultra-short pulse
characterization. In this paper, we prove that in order to determine a pair of
generic signals uniquely, up to trivial ambiguities, the number of phaseless
measurements one needs to collect is, at most, five times the number of
parameters required to describe the signals. This result improves significantly
upon previous papers, which required the number of measurements to be quadratic
in the number of parameters rather than linear.
  In addition, we consider the simpler problem of recovering a pair of generic
signals from their blind short-time Fourier transform, when the phases are
known. In this setting, which can be understood as a special case of the blind
deconvolution problem, we show that the number of measurements required to
determine the two signals, up to trivial ambiguities, equals exactly the number
of parameters to be recovered.
  As a side result, we study the classical phase retrieval problem---that is,
recovering a signal from its Fourier magnitudes---when some entries of the
signal are known apriori. We derive a bound on the number of required
measurements as a function of the size of the set of known entries.
Specifically, we show that if most of the signal's entries are known, then only
a few Fourier magnitudes are necessary to determine a signal uniquely.

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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn