Guarantees of total variation minimization for signal recovery

DOI10.1093/imaiai/iav009zbMath1387.94028arXiv1301.6791OpenAlexW2568311054MaRDI QIDQ4603592

Jian-Feng Cai, Weiyu Xu

Publication date: 16 February 2018

Published in: Information and Inference (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.6791

zbMATH Keywords

total variationphase transitionGaussian widthhigh dimensional geometry

Mathematics Subject Classification ID

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

Related Items

\(\ell^1\)-analysis minimization and generalized (co-)sparsity: when does recovery succeed?, A unified approach to uniform signal recovery from nonlinear observations, Sampling rates for \(\ell^1\)-synthesis, Block-sparse recovery of semidefinite systems and generalized null space conditions, Enhanced total variation minimization for stable image reconstruction, Reconstruction Methods in THz Single-Pixel Imaging, Improved Recovery Guarantees and Sampling Strategies for TV Minimization in Compressive Imaging

Cites Work

• Unnamed Item
• Unnamed Item
• Nonlinear total variation based noise removal algorithms
• A mathematical introduction to compressive sensing
• Compressed sensing with coherent and redundant dictionaries
• On total variation minimization and surface evolution using parametric maximum flows
• The restricted isometry property and its implications for compressed sensing
• Total variation based convex filters for medical imaging
• The cosparse analysis model and algorithms
• The convex geometry of linear inverse problems
• High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension
• Stable Image Reconstruction Using Total Variation Minimization
• Accurate Prediction of Phase Transitions in Compressed Sensing via a Connection to Minimax Denoising
• Robust Sparse Analysis Regularization
• Linear convergence rates for Tikhonov regularization with positively homogeneous functionals
• The Split Bregman Method for L1-Regularized Problems
• On sparse reconstruction from Fourier and Gaussian measurements
• 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?
• Split Bregman Methods and Frame Based Image Restoration
• Compressed Sensing and Redundant Dictionaries
• Highly Robust Error Correction byConvex Programming
• Stable Signal Reconstruction via $\ell^1$-Minimization in Redundant, Non-Tight Frames
• Sparse Error Correction From Nonlinear Measurements With Applications in Bad Data Detection for Power Networks
• A total variation enhanced modified gradient algorithm for profile reconstruction
• Living on the edge: phase transitions in convex programs with random data
• Precise Stability Phase Transitions for $\ell_1$ Minimization: A Unified Geometric Framework
• The Noise-Sensitivity Phase Transition in Compressed Sensing
• Image restoration: Total variation, wavelet frames, and beyond
• Near-Optimal Compressed Sensing Guarantees for Total Variation Minimization
• Neighborliness of randomly projected simplices in high dimensions
• Compressed sensing