Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recovery Analysis for Weighted $\ell_1$-Minimization Using a Null Space
  Property   We study the recovery of sparse signals from underdetermined linear
measurements when a potentially erroneous support estimate is available. Our
results are twofold. First, we derive necessary and sufficient conditions for
signal recovery from compressively sampled measurements using weighted
$\ell_1$-norm minimization. These conditions, which depend on the choice of
weights as well as the size and accuracy of the support estimate, are on the
null space of the measurement matrix. They can guarantee recovery even when
standard $\ell_1$ minimization fails. Second, we derive bounds on the number of
Gaussian measurements for these conditions to be satisfied, i.e., for weighted
$\ell_1$ minimization to successfully recover all sparse signals whose support
has been estimated sufficiently accurately. Our bounds show that weighted
$\ell_1$ minimization requires significantly fewer measurements than standard
$\ell_1$ minimization when the support estimate is relatively accurate.

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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
3
The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph