Corpus ID: 12816905

# Recoverability of Group Sparse Signals from Corrupted Measurements via Robust Group Lasso

@article{Wei2015RecoverabilityOG,
title={Recoverability of Group Sparse Signals from Corrupted Measurements via Robust Group Lasso},
author={Xiaohan Wei and Qing Ling and Zhu Han},
journal={ArXiv},
year={2015},
volume={abs/1509.08490}
}
• Published 2015
• Physics, Computer Science, Mathematics
• ArXiv
This paper considers the problem of recovering a group sparse signal matrix $\mathbf{Y} = [\mathbf{y}_1, \cdots, \mathbf{y}_L]$ from sparsely corrupted measurements $\mathbf{M} = [\mathbf{A}_{(1)}\mathbf{y}_{1}, \cdots, \mathbf{A}_{(L)}\mathbf{y}_{L}] + \mathbf{S}$, where $\mathbf{A}_{(i)}$'s are known sensing matrices and $\mathbf{S}$ is an unknown sparse error matrix. A robust group lasso (RGL) model is proposed to recover $\mathbf{Y}$ and $\mathbf{S}$ through simultaneously minimizing the… Expand
1 Citations

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#### References

SHOWING 1-10 OF 46 REFERENCES
Exact Recoverability From Dense Corrupted Observations via $\ell _{1}$-Minimization
• Mathematics, Computer Science
• IEEE Transactions on Information Theory
• 2013
It is confirmed that stable recovery is possible when measurements are polluted by both gross sparse and small dense errors, and shown that with high probability, ℓ<sub>1</sub>-minimization can recover the sparse signal of interest. Expand
Dense Error Correction Via $\ell^1$-Minimization
• Mathematics, Computer Science
• IEEE Transactions on Information Theory
• 2009
It is proved that for highly correlated (and possibly overcomplete) dictionaries A, any sufficiently sparse signal x can be recovered by solving an ℓ1 -minimization problem min ||x||1 + ||e||1 subject to y = Ax + e. Expand
Compressed Sensing and Matrix Completion with Constant Proportion of Corruptions
It is proved that one can recover an n×n low-rank matrix from m corrupted sampled entries by tractable optimization provided the rank is on the order of O(m/(nlog2n)); again, this holds when there is a positive fraction of corrupted samples. Expand
Compressed Sensing of Simultaneous Low-Rank and Joint-Sparse Matrices
• Computer Science, Mathematics
• ArXiv
• 2012
A new model is introduced that can efficiently restrict the degrees of freedom of the problem and is generic enough to find a lot of applications, for instance in multichannel signal compressed sensing and compressive sparse principal component analysis (s-PCA). Expand
Exact Matrix Completion via Convex Optimization
• Mathematics, Computer Science
• Found. Comput. Math.
• 2009
It is proved that one can perfectly recover most low-rank matrices from what appears to be an incomplete set of entries, and that objects other than signals and images can be perfectly reconstructed from very limited information. Expand
Robust Recovery of Signals From a Structured Union of Subspaces
• Computer Science, Physics
• IEEE Transactions on Information Theory
• 2009
This paper develops a general framework for robust and efficient recovery of nonlinear but structured signal models, in which x lies in a union of subspaces, and presents an equivalence condition under which the proposed convex algorithm is guaranteed to recover the original signal. Expand
Rank Awareness in Joint Sparse Recovery
• Computer Science, Mathematics
• IEEE Transactions on Information Theory
• 2012
This paper revisits the sparse multiple measurement vector (MMV) problem, where the aim is to recover a set of jointly sparse multichannel vectors from incomplete measurements and demonstrates that the rank aware techniques are significantly better than existing methods in dealing with multiple measurements. Expand
Group-Lasso on Splines for Spectrum Cartography
• Mathematics, Computer Science
• IEEE Transactions on Signal Processing
• 2011
A spline-based approach to field estimation, which relies on a basis expansion model of the field of interest, and induces a group-Lasso estimator for the coefficients of the thin-plate spline expansions per basis. Expand
Group sparse Lasso for cognitive network sensing robust to model uncertainties and outliers
• Computer Science
• Phys. Commun.
• 2012
A collaborative scheme whereby CRs cooperate to localize active primary user (PU) transmitters and reconstruct a power spectral density map portraying the spatial distribution of power across the monitored area per frequency band and channel coherence interval is developed. Expand
Block-Sparse Signals: Uncertainty Relations and Efficient Recovery
• Mathematics, Computer Science
• IEEE Transactions on Signal Processing
• 2010
The significance of the results presented in this paper lies in the fact that making explicit use of block-sparsity can provably yield better reconstruction properties than treating the signal as being sparse in the conventional sense, thereby ignoring the additional structure in the problem. Expand