204,810 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
Blind channel equalization using weighted subspace methods
This paper addresses the problems of blind channel estimation and symbol detection with second order statistics methods from the received data. It can be shown that this problem is similar to direction of arrival (DOA) estimation, where many solutions like the MUSIC algorithm orPeer ReviewedPostprint (published version
Estimating the system order by subspace methods
This paper discusses how to determine the order of a state-space model. To do so, we start by
revising existing approaches and find in them three basic shortcomings: i) some of them have a
poor performance in short samples, ii) most of them are not robust and iii) none of them can
accommodate seasonality. We tackle the first two issues by proposing new and refined criteria.
The third issue is dealt with by decomposing the system into regular and seasonal sub-systems.
The performance of all the procedures considered is analyzed through Monte Carlo simulations
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