Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Impact of the Sensing Spectrum on Signal Recovery in Generalized Linear
  Models   We consider a nonlinear inverse problem $\mathbf{y}= f(\mathbf{Ax})$, where
observations $\mathbf{y} \in \mathbb{R}^m$ are the componentwise nonlinear
transformation of $\mathbf{Ax} \in \mathbb{R}^m$, $\mathbf{x} \in \mathbb{R}^n$
is the signal of interest and $\mathbf{A}$ is a known linear mapping. By
properly specifying the nonlinear processing function, this model can be
particularized to many signal processing problems, including compressed sensing
and phase retrieval.
  Our main goal in this paper is to understand the impact of sensing matrices,
or more specifically the spectrum of sensing matrices, on the difficulty of
recovering $\mathbf{x}$ from $\mathbf{y}$. Towards this goal, we study the
performance of one of the most successful recovery methods, i.e. the
expectation propagation algorithm (EP). We define a notion for the spikiness of
the spectrum of $\mathbf{A}$ and show the importance of this measure in the
performance of the EP. Whether the spikiness of the spectrum can hurt or help
the recovery performance of EP depends on $f$. We define certain quantities
based on the function $f$ that enables us to describe the impact of the
spikiness of the spectrum on EP recovery. Based on our framework, we are able
to show that for instance, in phase-retrieval problems, matrices with spikier
spectrums are better for EP, while in 1-bit compressed sensing problems, less
spiky (flatter) spectrums offer better recoveries. Our results unify and
substantially generalize the existing results that compare sub-Gaussian and
orthogonal matrices, and provide a platform toward designing optimal sensing
systems.

26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas