On discrete \(\ell ^{1}\)-regularization

DOI10.1007/s10444-011-9247-7zbMath1271.65098OpenAlexW275888382MaRDI QIDQ1946524

Charles A. Micchelli, Tao Zhao

Publication date: 15 April 2013

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-011-9247-7

zbMATH Keywords

convex optimizationsparsitycompressed sensing\(l ^{1}\) approximationdiscrete \(l^1\)-regularization problemvector alternationvector equioscillation

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Numerical mathematical programming methods (65K05) Convex programming (90C25) Minimax problems in mathematical programming (90C47) Inequalities and extremum problems involving convexity in convex geometry (52A40)

Cites Work

• Sparse representations and approximation theory
• Almost Chebyshev properties for \(L^ 1\)-approximation of continuous functions
• Proximity algorithms for the L1/TV image denoising model
• Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing
• On n-Widths in L ∞
• Efficient Minimization Methods of Mixed l2-l1 and l1-l1 Norms for Image Restoration
• For most large underdetermined systems of linear equations the minimal 𝓁₁‐norm solution is also the sparsest solution
• Linear L ₁ Approximation for a Discrete Point Set and L ₁ Solutions of Overdetermined Linear Equations
• Finite dimensional convexity and optimization
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