202 research outputs found
Subspace Methods for Joint Sparse Recovery
We propose robust and efficient algorithms for the joint sparse recovery
problem in compressed sensing, which simultaneously recover the supports of
jointly sparse signals from their multiple measurement vectors obtained through
a common sensing matrix. In a favorable situation, the unknown matrix, which
consists of the jointly sparse signals, has linearly independent nonzero rows.
In this case, the MUSIC (MUltiple SIgnal Classification) algorithm, originally
proposed by Schmidt for the direction of arrival problem in sensor array
processing and later proposed and analyzed for joint sparse recovery by Feng
and Bresler, provides a guarantee with the minimum number of measurements. We
focus instead on the unfavorable but practically significant case of
rank-defect or ill-conditioning. This situation arises with limited number of
measurement vectors, or with highly correlated signal components. In this case
MUSIC fails, and in practice none of the existing methods can consistently
approach the fundamental limit. We propose subspace-augmented MUSIC (SA-MUSIC),
which improves on MUSIC so that the support is reliably recovered under such
unfavorable conditions. Combined with subspace-based greedy algorithms also
proposed and analyzed in this paper, SA-MUSIC provides a computationally
efficient algorithm with a performance guarantee. The performance guarantees
are given in terms of a version of restricted isometry property. In particular,
we also present a non-asymptotic perturbation analysis of the signal subspace
estimation that has been missing in the previous study of MUSIC.Comment: submitted to IEEE transactions on Information Theory, revised versio
Coherence-based Partial Exact Recovery Condition for OMP/OLS
We address the exact recovery of the support of a k-sparse vector with
Orthogonal Matching Pursuit (OMP) and Orthogonal Least Squares (OLS) in a
noiseless setting. We consider the scenario where OMP/OLS have selected good
atoms during the first l iterations (l<k) and derive a new sufficient and
worst-case necessary condition for their success in k steps. Our result is
based on the coherence \mu of the dictionary and relaxes Tropp's well-known
condition \mu<1/(2k-1) to the case where OMP/OLS have a partial knowledge of
the support
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
This paper demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal with nonzero entries in dimension given random linear measurements of that signal. This is a massive improvement over previous results, which require measurements. The new results for OMP are comparable with recent results for another approach called Basis Pursuit (BP). In some settings, the OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal recovery problems
Compressive Sensing Theory for Optical Systems Described by a Continuous Model
A brief survey of the author and collaborators' work in compressive sensing
applications to continuous imaging models.Comment: Chapter 3 of "Optical Compressive Imaging" edited by Adrian Stern
published by Taylor & Francis 201
Exact Recovery Conditions for Sparse Representations with Partial Support Information
We address the exact recovery of a k-sparse vector in the noiseless setting
when some partial information on the support is available. This partial
information takes the form of either a subset of the true support or an
approximate subset including wrong atoms as well. We derive a new sufficient
and worst-case necessary (in some sense) condition for the success of some
procedures based on lp-relaxation, Orthogonal Matching Pursuit (OMP) and
Orthogonal Least Squares (OLS). Our result is based on the coherence "mu" of
the dictionary and relaxes the well-known condition mu<1/(2k-1) ensuring the
recovery of any k-sparse vector in the non-informed setup. It reads
mu<1/(2k-g+b-1) when the informed support is composed of g good atoms and b
wrong atoms. We emphasize that our condition is complementary to some
restricted-isometry based conditions by showing that none of them implies the
other.
Because this mutual coherence condition is common to all procedures, we carry
out a finer analysis based on the Null Space Property (NSP) and the Exact
Recovery Condition (ERC). Connections are established regarding the
characterization of lp-relaxation procedures and OMP in the informed setup.
First, we emphasize that the truncated NSP enjoys an ordering property when p
is decreased. Second, the partial ERC for OMP (ERC-OMP) implies in turn the
truncated NSP for the informed l1 problem, and the truncated NSP for p<1.Comment: arXiv admin note: substantial text overlap with arXiv:1211.728
Distributed Compressive CSIT Estimation and Feedback for FDD Multi-user Massive MIMO Systems
To fully utilize the spatial multiplexing gains or array gains of massive
MIMO, the channel state information must be obtained at the transmitter side
(CSIT). However, conventional CSIT estimation approaches are not suitable for
FDD massive MIMO systems because of the overwhelming training and feedback
overhead. In this paper, we consider multi-user massive MIMO systems and deploy
the compressive sensing (CS) technique to reduce the training as well as the
feedback overhead in the CSIT estimation. The multi-user massive MIMO systems
exhibits a hidden joint sparsity structure in the user channel matrices due to
the shared local scatterers in the physical propagation environment. As such,
instead of naively applying the conventional CS to the CSIT estimation, we
propose a distributed compressive CSIT estimation scheme so that the compressed
measurements are observed at the users locally, while the CSIT recovery is
performed at the base station jointly. A joint orthogonal matching pursuit
recovery algorithm is proposed to perform the CSIT recovery, with the
capability of exploiting the hidden joint sparsity in the user channel
matrices. We analyze the obtained CSIT quality in terms of the normalized mean
absolute error, and through the closed-form expressions, we obtain simple
insights into how the joint channel sparsity can be exploited to improve the
CSIT recovery performance.Comment: 16 double-column pages, accepted for publication in IEEE Transactions
on Signal Processin
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