Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Support Recovery of Jointly Sparse Gaussian Sources using Sparse
  Bayesian Learning   In this work, we provide non-asymptotic, probabilistic guarantees for
successful recovery of the common nonzero support of jointly sparse Gaussian
sources in the multiple measurement vector (MMV) problem. The support recovery
problem is formulated as the marginalized maximum likelihood (or type-II ML)
estimation of the variance hyperparameters of a joint sparsity inducing
Gaussian prior on the source signals. We derive conditions under which the
resulting nonconvex constrained optimization perfectly recovers the nonzero
support of a joint-sparse Gaussian source ensemble with arbitrarily high
probability. The support error probability decays exponentially with the number
of MMVs at a rate that depends on the smallest restricted singular value and
the nonnegative null space property of the self Khatri-Rao product of the
sensing matrix. Our analysis confirms that nonzero supports of size as high as
O($m^2$) are recoverable from $m$ measurements per sparse vector. Our derived
sufficient conditions for support consistency of the proposed constrained
type-II ML solution also guarantee the support consistency of any global
solution of the multiple sparse Bayesian learning (M-SBL) optimization whose
nonzero coefficients lie inside a bounded interval. For the case of noiseless
measurements, we further show that a single MMV is sufficient for perfect
recovery of the $k$-sparse support by M-SBL, provided all subsets of $k + 1$
columns of the sensing matrix are linearly independent.

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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin