Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the gap between RIP-properties and sparse recovery conditions   We consider the problem of recovering sparse vectors from underdetermined
linear measurements via $\ell_p$-constrained basis pursuit. Previous analyses
of this problem based on generalized restricted isometry properties have
suggested that two phenomena occur if $p\neq 2$. First, one may need
substantially more than $s \log(en/s)$ measurements (optimal for $p=2$) for
uniform recovery of all $s$-sparse vectors. Second, the matrix that achieves
recovery with the optimal number of measurements may not be Gaussian (as for
$p=2$). We present a new, direct analysis which shows that in fact neither of
these phenomena occur. Via a suitable version of the null space property we
show that a standard Gaussian matrix provides $\ell_q/\ell_1$-recovery
guarantees for $\ell_p$-constrained basis pursuit in the optimal measurement
regime. Our result extends to several heavier-tailed measurement matrices. As
an application, we show that one can obtain a consistent reconstruction from
uniform scalar quantized measurements in the optimal measurement regime.

20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph