Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact recoverability from dense corrupted observations via $L_1$
  minimization   This paper confirms a surprising phenomenon first observed by Wright
\textit{et al.} \cite{WYGSM_Face_2009_J} \cite{WM_denseError_2010_J} under
different setting: given $m$ highly corrupted measurements $y = A_{\Omega
\bullet} x^{\star} + e^{\star}$, where $A_{\Omega \bullet}$ is a submatrix
whose rows are selected uniformly at random from rows of an orthogonal matrix
$A$ and $e^{\star}$ is an unknown sparse error vector whose nonzero entries may
be unbounded, we show that with high probability $\ell_1$-minimization can
recover the sparse signal of interest $x^{\star}$ exactly from only $m = C
\mu^2 k (\log n)^2$ where $k$ is the number of nonzero components of
$x^{\star}$ and $\mu = n \max_{ij} A_{ij}^2$, even if nearly 100% of the
measurements are corrupted. We further guarantee that stable recovery is
possible when measurements are polluted by both gross sparse and small dense
errors: $y = A_{\Omega \bullet} x^{\star} + e^{\star}+ \nu$ where $\nu$ is the
small dense noise with bounded energy. Numerous simulation results under
various settings are also presented to verify the validity of the theory as
well as to illustrate the promising potential of the proposed framework.

33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con