3,088 research outputs found
Improving Noise Robustness in Subspace-based Joint Sparse Recovery
In a multiple measurement vector problem (MMV), where multiple signals share
a common sparse support and are sampled by a common sensing matrix, we can
expect joint sparsity to enable a further reduction in the number of required
measurements. While a diversity gain from joint sparsity had been demonstrated
earlier in the case of a convex relaxation method using an mixed norm
penalty, only recently was it shown that similar diversity gain can be achieved
by greedy algorithms if we combine greedy steps with a MUSIC-like subspace
criterion. However, the main limitation of these hybrid algorithms is that they
often require a large number of snapshots or a high signal-to-noise ratio (SNR)
for an accurate subspace as well as partial support estimation. One of the main
contributions of this work is to show that the noise robustness of these
algorithms can be significantly improved by allowing sequential subspace
estimation and support filtering, even when the number of snapshots is
insufficient. Numerical simulations show that a novel sequential compressive
MUSIC (sequential CS-MUSIC) that combines the sequential subspace estimation
and support filtering steps significantly outperforms the existing greedy
algorithms and is quite comparable with computationally expensive state-of-art
algorithms
Sparsity-Based Error Detection in DC Power Flow State Estimation
This paper presents a new approach for identifying the measurement error in
the DC power flow state estimation problem. The proposed algorithm exploits the
singularity of the impedance matrix and the sparsity of the error vector by
posing the DC power flow problem as a sparse vector recovery problem that
leverages the structure of the power system and uses -norm minimization
for state estimation. This approach can provably compute the measurement errors
exactly, and its performance is robust to the arbitrary magnitudes of the
measurement errors. Hence, the proposed approach can detect the noisy elements
if the measurements are contaminated with additive white Gaussian noise plus
sparse noise with large magnitude. The effectiveness of the proposed
sparsity-based decomposition-DC power flow approach is demonstrated on the IEEE
118-bus and 300-bus test systems
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
Accelerated Cardiac Diffusion Tensor Imaging Using Joint Low-Rank and Sparsity Constraints
Objective: The purpose of this manuscript is to accelerate cardiac diffusion
tensor imaging (CDTI) by integrating low-rankness and compressed sensing.
Methods: Diffusion-weighted images exhibit both transform sparsity and
low-rankness. These properties can jointly be exploited to accelerate CDTI,
especially when a phase map is applied to correct for the phase inconsistency
across diffusion directions, thereby enhancing low-rankness. The proposed
method is evaluated both ex vivo and in vivo, and is compared to methods using
either a low-rank or sparsity constraint alone. Results: Compared to using a
low-rank or sparsity constraint alone, the proposed method preserves more
accurate helix angle features, the transmural continuum across the myocardium
wall, and mean diffusivity at higher acceleration, while yielding significantly
lower bias and higher intraclass correlation coefficient. Conclusion:
Low-rankness and compressed sensing together facilitate acceleration for both
ex vivo and in vivo CDTI, improving reconstruction accuracy compared to
employing either constraint alone. Significance: Compared to previous methods
for accelerating CDTI, the proposed method has the potential to reach higher
acceleration while preserving myofiber architecture features which may allow
more spatial coverage, higher spatial resolution and shorter temporal footprint
in the future.Comment: 11 pages, 16 figures, published on IEEE Transactions on Biomedical
Engineerin
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