PHASE TRANSITIONS IN ERROR CORRECTING AND COMPRESSED SENSING BY ℓ1 LINEAR PROGRAMMING
DOI10.1142/S0219691313600047zbMath1279.94040OpenAlexW2087286870MaRDI QIDQ2868199
Ryuichi Ashino, Rémi Vaillancourt
Publication date: 27 December 2013
Published in: International Journal of Wavelets, Multiresolution and Information Processing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s0219691313600047
numerical resultsphase transitioncompressed sensingerror correcting codemean breakdown points\(\ell _{1}\) linear programmingsparse corruption
Numerical mathematical programming methods (65K05) Signal theory (characterization, reconstruction, filtering, etc.) (94A12)
Cites Work
- Breakdown of equivalence between the minimal \(\ell^1\)-norm solution and the sparsest solution
- High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension
- Atomic Decomposition by Basis Pursuit
- Mean breakdown points for compressed sensing by uniformly distributed matrices
- Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
- Decoding by Linear Programming
- Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
- Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing
- Atomic Decomposition by Basis Pursuit
- Uncertainty principles and ideal atomic decomposition
- Exponential Bounds Implying Construction of Compressed Sensing Matrices, Error-Correcting Codes, and Neighborly Polytopes by Random Sampling
- For most large underdetermined systems of equations, the minimal 𝓁1‐norm near‐solution approximates the sparsest near‐solution
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