Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Necessary and Sufficient Conditions on Sparsity Pattern Recovery   The problem of detecting the sparsity pattern of a k-sparse vector in R^n
from m random noisy measurements is of interest in many areas such as system
identification, denoising, pattern recognition, and compressed sensing. This
paper addresses the scaling of the number of measurements m, with signal
dimension n and sparsity-level nonzeros k, for asymptotically-reliable
detection. We show a necessary condition for perfect recovery at any given SNR
for all algorithms, regardless of complexity, is m = Omega(k log(n-k))
measurements. Conversely, it is shown that this scaling of Omega(k log(n-k))
measurements is sufficient for a remarkably simple ``maximum correlation''
estimator. Hence this scaling is optimal and does not require more
sophisticated techniques such as lasso or matching pursuit. The constants for
both the necessary and sufficient conditions are precisely defined in terms of
the minimum-to-average ratio of the nonzero components and the SNR. The
necessary condition improves upon previous results for maximum likelihood
estimation. For lasso, it also provides a necessary condition at any SNR and
for low SNR improves upon previous work. The sufficient condition provides the
first asymptotically-reliable detection guarantee at finite SNR.

27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: stat
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom