Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase Retrieval Versus Phaseless Reconstruction   In 2006, Balan/Casazza/Edidin \cite{BCE} introduced the frame theoretic study
of phaseless reconstruction. Since then, this has turned into a very active
area of research. Over the years, many people have replaced the term {\it
phaseless reconstruction} with {\it phase retrieval}. Casazza then asked: {\it
Are these really the same?} In this paper, we will show that phase retrieval is
equivalent to phaseless reconstruction. We then show, more generally, that
phase retrieval by projections is equivalent to phaseless reconstruction by
projections. Finally, we study {\it weak phase retrieval} and discover that it
is very different from phaseless reconstruction.

33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci