Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Sharp Condition for Exact Support Recovery of with Orthogonal Matching
  Pursuit   Support recovery of sparse signals from noisy measurements with orthogonal
matching pursuit (OMP) has been extensively studied. In this paper, we show
that for any $K$-sparse signal $\x$, if a sensing matrix $\A$ satisfies the
restricted isometry property (RIP) with restricted isometry constant (RIC)
$\delta_{K+1} < 1/\sqrt {K+1}$, then under some constraints on the minimum
magnitude of nonzero elements of $\x$, OMP exactly recovers the support of $\x$
from its measurements $\y=\A\x+\v$ in $K$ iterations, where $\v$ is a noise
vector that is $\ell_2$ or $\ell_{\infty}$ bounded. This sufficient condition
is sharp in terms of $\delta_{K+1}$ since for any given positive integer $K$
and any $1/\sqrt{K+1}\leq \delta<1$, there always exists a matrix $\A$
satisfying the RIP with $\delta_{K+1}=\delta$ for which OMP fails to recover a
$K$-sparse signal $\x$ in $K$ iterations. Also, our constraints on the minimum
magnitude of nonzero elements of $\x$ are weaker than existing ones. Moreover,
we propose worst-case necessary conditions for the exact support recovery of
$\x$, characterized by the minimum magnitude of the nonzero elements of $\x$.

37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph