Perturbations of measurement matrices and dictionaries in compressed sensing

DOI10.1016/j.acha.2011.12.002zbMath1256.94015OpenAlexW2083587165MaRDI QIDQ442524

Alexander M. Powell, Xuemei Chen, Akram Al-Droubi

Publication date: 1 August 2012

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.acha.2011.12.002

zbMATH Keywords

stabilityredundant dictionarysparse representationcompressed sensing

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12)

Related Items (17)

Sparse Model Uncertainties in Compressed Sensing with Application to Convolutions and Sporadic Communication ⋮ Iterative hard thresholding for compressed data separation ⋮ Stability of lq-analysis based dual frame with Weibull matrices for 0 < q ≤ 1 ⋮ Stable recovery of weighted sparse signals from phaseless measurements via weighted l₁ minimization ⋮ Analysis \(\ell_1\)-recovery with frames and Gaussian measurements ⋮ On the null space property of \(l_q\)-minimization for \(0 < q \leq 1\) in compressed sensing ⋮ Sparse recovery in probability via \(l_q\)-minimization with Weibull random matrices for \(0 < q\leq 1\) ⋮ The \( \ell _1 \)-analysis in phase retrieval with redundant dictionary ⋮ Sparse recovery with coherent tight frames via analysis Dantzig selector and analysis LASSO ⋮ Iterative re-weighted least squares algorithm for \(l_p\)-minimization with tight frame and \(0 < p \leq 1\) ⋮ A null space analysis of the \(\ell_1\)-synthesis method in dictionary-based compressed sensing ⋮ Inpainting via sparse recovery with directional constraints ⋮ New conditions on stable recovery of weighted sparse signals via weighted \(l_1\) minimization ⋮ Preserving injectivity under subgaussian mappings and its application to compressed sensing ⋮ Perturbation analysis of \(L_{1-2}\) method for robust sparse recovery ⋮ Optimal RIP bounds for sparse signals recovery via \(\ell_p\) minimization ⋮ Optimal \(D\)-RIP bounds in compressed sensing

Cites Work

• Compressed sensing with coherent and redundant dictionaries
• Sparse recovery under matrix uncertainty
• Highly sparse representations from dictionaries are unique and independent of the sparseness measure
• Sparse recovery by non-convex optimization - instance optimality
• A note on guaranteed sparse recovery via \(\ell_1\)-minimization
• Real versus complex null space properties for sparse vector recovery
• Sparsest solutions of underdetermined linear systems via \( \ell _q\)-minimization for \(0<q\leqslant 1\)
• Optimally Sparse Representations of 3D Data with $C^2$ Surface Singularities Using Parseval Frames of Shearlets
• Compressed sensing and best 𝑘-term approximation
• Restricted isometry properties and nonconvex compressive sensing
• Decoding by Linear Programming
• Sparse representations in unions of bases
• Compressed Sensing and Redundant Dictionaries
• Sparse Approximation Property and Stable Recovery of Sparse Signals From Noisy Measurements
• Sparse Recovery From Combined Fusion Frame Measurements
• Stable signal recovery from incomplete and inaccurate measurements
• Compressed sensing

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