Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reconstructing real-valued functions from unsigned coefficients with
  respect to wavelet and other frames   In this paper we consider the following problem of phase retrieval: Given a
collection of real-valued band-limited functions
$\{\psi_{\lambda}\}_{\lambda\in \Lambda}\subset L^2(\mathbb{R}^d)$ that
constitutes a semi-discrete frame, we ask whether any real-valued function $f
\in L^2(\mathbb{R}^d)$ can be uniquely recovered from its unsigned convolutions
${\{|f \ast \psi_\lambda|\}_{\lambda \in \Lambda}}$.
  We find that under some mild assumptions on the semi-discrete frame and if
$f$ has exponential decay at $\infty$, it suffices to know $|f \ast
\psi_\lambda|$ on suitably fine lattices to uniquely determine $f$ (up to a
global sign factor).
  We further establish a local stability property of our reconstruction
problem. Finally, for two concrete examples of a (discrete) frame of
$L^2(\mathbb{R}^d)$, $d=1,2$, we show that through sufficient oversampling one
obtains a frame such that any real-valued function with exponential decay can
be uniquely recovered from its unsigned frame coefficients.

13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom